After you complete a dungeon, can you go back to the town in the area the dungeon is in, and can you redo the dungeon?

You can redo dungeons daily. You don't even need to go back to town just clear the dungeon one day and at midnight you'll be allowed to clear it again.

I read somewhere that you can't go back to the town in the dungeon you've finished region. (Ex. I finish Nightfall Bandit dungeon, Would I still be able to access the town Esior's Haven)

You will always be able to re-enter a town, even after finishing that region. So even though you compelted the bandit dungeon, you can still access the town.

I do the night fall dungeon daily and I'm always going to town there for missions, nets, and random healing when the price would be to much for potions to deal with reasonably, and you can even go to town while in the dungeon and buy stuff as long as your not in battle

Thanks!

Yes, you can reenter the town after completing a dungeon. :p You just cannot reenter the dungeon, itself, until the midnight after completing it (and there after ).

Edit: XD Late response.