What you are looking for is "Crawl Stone Soup". It generates new dungeons every play, but once a level has been generated, it is persistant.
It is very anti-grinding too. For example, it has shops in the dungeon, but you cannot sell items. So items are worthless unless you really need them.
It also has "branches", every level has 3 up staircases, and 3 downstaircases. If you have fully explored a level and only have 2 down-staircases it means that there is a part of this level you haven't found yet. One way to find it is to go back up, and try all the 3 down-staircases there, or go down and try all the 3 up-staircases from there.
You start at level 1 in the dungeon, there is no town with shops, but I think you will like it
I do reccomend you play the Stone Soup version of Crawl instead of the original version though, because the controls of Stone Soup is MUCH more convenient and makes the game more fun to play!