Well he'd still have to send soldiers in as from what I understand Amalasuntha wasn't that popular among the Ostrogoths.
It still probably wouldn't be as destructive as OTL.
I agree. Glossing over the various Gothic War etc wiki pages to help refresh my memory, I would expect something like this:
Places firmly in the Amalasuntha/Justinian camp
Sicily - pro-Empire population, defected almost without a fight OTL (sans one die-hard garrison)
Rome/Latium - Roman elites have the advantage of having the sizeable urban mob at their disposal, a fact which would surely influence the local commander re: which side to choose. Sided with the Empire OTL as soon as Belisarius arrived with a handful of men
Salona/Illirya - reported to have a pro-Empire population and very close to the main imperial army located right across the border (on the other hand, the Goths can easily reinforce at the expense of other theaters if they so choose - a fact demonstrated by OTL)
Places leaning towards Amalasuntha/Justinian
Milan - second largest city in the peninsula with a large Roman population, sided with the Empire OTL (with disastrous consequences). However, surrounded by pro-Gothic areas, so may bid its time
Tuscany - domain of Theodahad, who, ironically, may side with Amalasuntha here given strong enough initial moves by Justinian
Places leaning towards Gothic independence
Naples - resisted Belisarius (bad move Naples) on account of two Gothic orators and whilst thinking a large Gothic army was approaching, despite having a mostly Roman population
Ravenna - Probably a large number of Gothic soldiers and noblemen will be in or near the city, meaning resistance is likely. However, also boasts a large Roman population and high concentration of Roman and Romano-Gothic elites, and easily reachable by ship from Greece. In the unlikely chance that Justinian wins an early victory here, a swift and decisive campaign is almost assured, as everyone who is on the fence would gain every reason to pick the winning team. Defeat will likely mean the war gets dragged on.
Venice/Istria - home of the Rugii, who where very apartheid-ish when it came to mixing with Goths. Both Eraric and Totila negotiated with Justinian OTL. However, the former was assassinated and the latter decided to got with the flow of continued Gothic resistance
Places firmly in the Gothic independence camp
Northern Italy - features the highest density of Gothic population, especially north of the Po. Expect towns like Verona or Ticinum to be the last ones holding out.