Lombardy, although landlocked, would be far better, but it requires compensation for Austria in Germany and, as others have said it is easier for other powers to just let Austria have Italy as her own playground than giving her a bigger share of Germany.
But let's handwave this for a moment: how would Risorgimento change? I think Sardinia will become Austrian aligned in this scenario, especially if/when France gets rids of the Bourbons again, but this will cause internal instability, especially in Genoa, which will want Milanese trade to pass through her port.
The relationship with the Duchies? Although austrian clients they were not strictly puppets and often acted with some independence, esoecially Tuscany: Leghorn is another possibility for a friendly port for Milan: a common trade zone between Lombardy, Parma, Modena and Tuscany makes a great deal of sense and could be an interesting nucleus for a unification that is more a coalescence than a conquest.
In the game of musical thrones played at the Congress of Vienna there were always a few musical chairs missing, even keeping into account the elimination of the former Italian republics (Venice, Genoa and Lucca - it is interesting that the 4 Free Cities in Northern Germany were allowed to remain independent under a republican system). Then there is the problem with Austria, who wanted (and obtained) a free hand in Italy, through direct annexations (Venetia, in addition to the former possessions in Lombardy) and states ruled by princes with Habsburg dynastic ties (Modena, Tuscany and Parma - although the last one was during the lifetime of Marie Louise only). The remaining Italian states (Sardinia, Two Sicilies and Papal States) were formally independent but quite conscious that their survival was pretty much predicated on remaining in good terms with Austria, who was appointed by the Powers as the guarantor in Italy of the Restauration. No other of the 5 Powers was interested in getting involved in Italy. It is very difficult (if not almost impossible) to foresee a different arrangement from what was agreed in Vienna unless something major happens (like the unlikely war over Saxony) with two possible exceptions: Romagna, Marche and the Papal Legations of Bologna and Ferrara might be carved out and made into an "independent" state (this was discussed in Vienna, but there was no one strongly arguing for it, and the default was to re-create the Papal States in their pre-Napoleonic extension. Twenty years later Metternich regretted this decision, since the Papal government was an awful mess even by reactionary standards, but it was too late), and the kingdom of Naples might remain under Murat's rule provided that Murat shows he's worth of it.
IMHO Murat has far better chances than Eugene to keep a crown, if he can keep his head down and does not rock the boat: given Murat's personality, it is a big call. The only real chance is that he follows his wife's early advice to switch sides.
Eugene is in a worse cleft because of the geographical location of his power base (I'm generous), but he also has to keep his head down and prove he can be an asset. His only advantage is in the marital ties with Bavaria: same thing as with Murat, follow the wifey advice and switch sides. It is almost more difficult than it would be for Murat. If he manages all that, the only realistic hope is the partition of the Papal States: anything more cannot be argued on a rational basis.
It is difficult to answer a very sketchy hypothetical scenario: a Beauharnais Lombardy would certainly have some impact on the Italian situation, and even beyond that, but which kind of impact will depend on what happens between 1815 and say 1840. I do not see any particular reason to see major changes in the history of Piedmont-Sardinia (unless you want to posit an early death of Charles Albert), nor in the rest of Italy. Hopefully Eugene and his heir will be able to give some boost to the economy in their possessions, and increase commerce with Switzerland and Northern Europe (Bavaria in particular), but they will have to play a very cautious game on the political side: Austrians troops can be in Milan very quickly, and Sardinians too. I am very skeptic about a customs union: the only Italian ruler who could show an interest is the Grand-duke of Tuscany; Parma does not gives anyone the time of the day without Austrian permission, and the awful backstabber who is on the throne of Modena is scarcely more free to act on his own; nothing good can come either from Naples or from Rome (let's assume the papal succession is not modified). There might be more interest in a customs union with Sardinia (as you note the bulk of import/export from Lombardy should go through Genoa), but to get a real boost there is the need of a railway link so we go to mid-1840s at best (and assume there is no Austrian veto, nor Eugene's heir is worried by the railway link with Piedmont, given the centuries-old Savoy ambitions to take Milan.
OTOH interesting things might happen in TTL 1848-equivalent (which I believe it is very difficult to butterfly away, and should reasonably happen at the same time given the bed harvests in 1846-47). If (and it is a very big if) Piedmont-Sardinia and Lombardy have improved the respective economies by close cooperation, there is a railway link to Milan and beyond and Charles Albert is a bit more confident there can be Lombard and Sardinian troops very quickly on the Mincio, Modena, Parma and Romagna would go up in insurrection and Leopold of Tuscany might join the Italian League. Since I'm butterflying away the month thrown away by Charles Albert's dithering, the war in Northern Italy might end up quite differently. There is still the Quadrilateral (where Radetzky may or may not be in charge) but its lines of supply would be cut and sooner or later would have to come out. A very, very optimistic scenario but the best I can do and a possibility to go for a Federal Italy.
Actually poor Prina was beaten/stabbed to death with umbrellas iirc... Eugene was too honest for his own good: he should have jumped ship when his Bavarian in-laws did, but his positions in Italy were also too strategical to enable some sort of neutrality.
The whole attempt at coronation was a desperate gambit, mainly orchestrated by Melzi d'Eril and the reason to have Eugene as king is that basically there is no alternative for independence, the ones who ousted him thought that the powers would grant them independence an aristocratic-friendly constitution and a German prince, but they were as deluded ad Eugene: once the army guarding the Mincio dissolved, Bellegarde didn't have any second thougths before dissolving the aristocratic provisional government and occupying Milan. The same happened with Genoa, which was promised by Bentinck a restoration of the republic or at least independence, but than was sacrificed to the Savoia to make an anti-french buffer state.
It's a bit of a stretch, but if Eugene had taken a leaf from the tactics of his stepfather (a whiff of grapeshot) the coup might have worked. Its success (coupled with a political U-turn by asking to join the Coalition) would have improved the overall chances of Eugene. Ideally this would happen after Eugene had alrady opened channels with the Coalition, maybe using the good offices of his father-in-law
I agree with most of the posters here that it's very, very difficult. If Eugene jumps ship with his Bavarian in-laws, as suggested many times here, then maybe one thing that can happen is that a Kingdom of Italy could be formed with similar borders to OTL Kingdom of Lombardy-Venetia, with the Austrian Emperor as King, and Milan as a fief for Eugene as Duke of Lombardy under the overlordship of the Emperor as King of Italy. This gives Venice, and possibly Bologna and Marche, to Austria as compensation, and creates an Austrian-controlled block that can keep Eugene under control if he gets too independent for Austria's tastes. Let's remember they felt free to intervene as far as Naples when they thought the Liberals were getting too uppity there.
Eugene is going to have to toe the line: no Constitution, no economic reforms, no appeals or propaganda for Italian nationalism. If Eugene does as much as sneeze too close to the Liberals, he's going to be kicked out.
If the objective is to give Eugene a crown, any crown, then he'd be better off with Naples, if and only if he switches sides early enough. This requires a POD for Napoleon to place someone else trustworthy as viceroy in Milan, and I don't think he'll just swap Eugene with Murat.
After the dissolution of the HRE there is no "kingdom of Italy", and I believe that if Austria had tried to go for such a solution (which frankly does not give her any real benefit) there would be a strong opposition by the other Powers (and by all the Italian states too). I don't think that Eugene as duke of Milan under Austrian overlordship is practicable.
On paper, the throne of Naples would appear to be easier but once again there would be strong opposition (the Bourbons, their British protectors, France and even Spain), no real reason to do it and in the unlikely case it happens poor Eugene would be in a world of hurt and pain, being parachuted into a reality he does not know at all and where he has not the minimal power basis.
I stand by my opinion that the least ASBish throne Eugene may gain would have to be carved out of the Papal States: Romagna, Marche and the Legations. He still would have not much of a power basis, but at least it would be more similar to his previous experience as viceroy of Italy.
I meant to say that the acquisition of the Republic of Venice territories woth the treaty of Campoformido was not more legitimate that other territorial changes which happened during the Napoleonic period from a legitimacy/restoration point of view, but Bellegarde had conquered most of Veneto back fom the Franco Italians in 1814.