Oh boy...I'm going to REALLY have to dig deep into memory for this question. If I had to pick one from each game.
1: I remember liking Peach's Birthday Cake a lot.
2: Space Land, definitely.
3: Deep Bloobler Sea...I swear that second B looks like a typo.
4: Goomba's Casino Gala. This board just has so much to do despite having a very overarching luck-based gimmick involved.
Advance: Uhwhatboard. Though if I had to say, the Town Area was my favorite place in the game.
5: Rainbow Dream, no question. I like most of the boards in 5 though.
6: E. Gadd's Garage. Again, no doubt about this one, but I like most of the boards.
7: I fondly remember Neon Heights and Windmillville.
8: Shy Guy's Perplex Express. A nod back to the Excess Express in TTYD and a pretty unique board in its own right.
DS: I'd love to say Pinball Machine, but it is REALLY easy to get luckscrewed there. So Kamek's Library.
9: Magma Mine. This is probably the one time in MP9/MP10 where "Half your ministars" is actually okay as a gimmick! I have to give it credit for that. Even then, it's still a fun board.
MPIT: Star-Crossed Skyway. It feels like the only board done right in this game. (Note: This is the only Mario Party I do not own.)
MP10: Airs- Wait, "NOT including Mario Party 10." Never mind zel.