Dresden Germany somehow does not get bombed during WW2. Does it become a regional or even national capital (or a tourist trap!)?
1. Dresden has always been and is a regional capital (state capital of Saxony). But it stands no chance to become national capital. First of all, it is outside of the FRG, and the GDR will not let the chance down to make Ost-Berlin its capital.
Only if for some reason the Western powers can deny the GDR the use of Ost-Berlin, Dresden stands a chance (though I could imagine that the SED might decide to go to nearby Potsdam and wait until they can move back to Berlin). This would have its own set of implications, though. Due to Ulbricht's strong Saxon accent, this dialect was seen as a kind of "Communist rule language" (which is a bit mean). Pushing the capital into Saxony might reinforce regional antagonism and rivalries within the GDR.
2. In 1939, Dresden had 629,000 inhabitants. This dropped below 500,000 and it remained around this number until recent years when it rose above 520,000.
Demographically, it has suffered from WW2, without the bombardment, it might have maybe more inhabitants. With so much intact living space, there might be an urge to put a lot of refugees into the city.
Mind you: most of the ten thousands of people killed during the bombardment were not natives, but refugees from the East which had just poured into the city. Also, not all of the lost population between 1939 and 1950 is due to bombardment; there are also killed soldiers, killed Jews and evacuees which chose not to return.
And: not being bombed doesn't safe Dresden from finding itself in the Soviet zone resp. GDR. That itself has a demographic negative effect. Low birth rates. Lots of migration towards the GDR.
OTL, Dresden is #11 among Germany's most populated cities. I think an unbombed Dresden would at least be at 630,000 (assuming only a slight drop from 1939-50 and henceforth assuming similar growth/stagnation), that would carry her to a #6 position (and what is more, clearly ahead of its local rival Leipzig)....but certainly not to more than 700,000. Then it would today be German's largest non-million city, 5th after Berlin, Hamburg, Munich and Cologne, ahead of Frankfurt and Stuttgart.
3. Dresden is a major tourist destination due to the reconstruction efforts in GDR times and afterwards (they still work to make parts of the inner city ressemble the pre-war architecture more), but as a major city it is definitely not a tourist trap. It is a city definitely worth seeing and whenever you get the chance, I urge you to see it. However, as most major landmarks stand again, there wouldn't be much more of an appeal than OTL by now.
A larger city might even be detrimental to its appeal. The GDR had a habit of destroying stuff it disliked, or to let historic houses decay. Also, a larger Dresden would suffer more suburban spread into the very attractive landscape around the city.