In a sense, yeah. If you define 'town' as an area with a bunch of NPCs and the full set of shops with unique equipment, there seems to be one in each chapter so far although they're generally small compared to the giant sprawl of the hub town which seems to have all of the main buildings, the combat practice area (with infinite puzzle mode) and the museum as well as a dozen or so houses and other things.
Another interesting thing I didn't realize until I started playing it rather than watching is that the areas work kind of like Soul Blazer, if anyone's familiar with that game. You enter a town and it's completely empty so you go into the dungeon/combat zone and as you save toads they trickle back into the town and become the shopkeepers and random NPCs. It's a nice change from them just being the numeric statistic they were in Paper Jam. The way the game hides toads is interesting too - they're often disguised as some bit of origami that you need to hammer the crap out of to cause it to unfold into a flat sheet of paper, which has the toad on the other side. Making flowers grow to attract an origami butterfly and then hammering the butterfly so it unfolds into a toad and having the toad scream at you that he can't fly anymore and hop around waving his arms with a pissed expression on his face is miles better than a shitty pop culture pun.
One of the most amusing ones so far is in a patch of half-buried toads who all make dumb puns or do the standard thank-you-mario rambling when you pull them out. The last one is just the tip of a hand just barely sticking out of the ground and when you pull him out, all he says is "They buried me deepest because I'm the one they're afraid of." before leaving.
As for references to other games, it's similar to Mario Odyssey. There's a smattering of random 'I get that reference!!' Mario stuff but nothing Paper Mario specific so far. There is a carbon copy of the Link's Awakening fishing game though, which is hinted to be a recurring thing and has a scoreboard for fish sizes.