Mario Party Advance has a pretty decent single-player campaign, as it's dedicated with a single player in mind and I think it has lots of fun little quips and interactions with a wide variety of Mario characters. It doesn't really play like a traditional Mario Party game as well, being more focused on completing those tasks than playing minigames or buying stars or competing with others.
Mario Party DS has a decent amount of collectibles to focus on collecting, so I enjoy that as well, even if completing the Story Mode with all six characters can be tedious if you want to unlock everything.
If Mario Party: Island Tour had just Bowser Tower and scrapped its bad boards to focus just on that, I may have sorta recommended it as well, but as it is, I think it's too bare of a game to recommend to anyone (it doesn't have a bunch of collectibles worth collecting like DS does) and it contains awful board mechanics regardless that boil down to luck.
Most Mario Party single player modes are just, beat the CPU in a bunch of boards with traditional Mario Party rules, and some of them such as Mario Party 4 require you to do through with each character if you want to unlock all collectibles. It's pretty difficult recommending one with a single player in mind since that's not the series' focus.