Stage 2: This is tricky as they rarely stand out, and it's also the least-played stage in any game, since it's too early to need much practice but it's past the restart-fest of Stage 1. I'm going to go with EoSD as it's nice and relaxing, and Cirno's theme is the first really great theme in the series. (Not the best Stage 2 theme, though -- that goes to Parsee.)
Stage 3: MoF for this one. It's tricky to navigate the bullets and get a lot of items at max value, but it's a stage where you can feel the difference as your skill improves, and it's really satisfying to pull off. The Gensokyo the Gods Loved is outstanding. Nitori is a pretty decent boss, with only her midboss card and final being annoying.
Stage 4: This tends to be the most painful stage in any game. I'll go with PCB because it looks very intimidating, but a lot of it is just aimed stuff that's simple to dodge when you know what you're doing. Great themes for both the stage and boss, and some nice variety with the sisters' unique attacks.
Stage 5: Easily MoF, also my favourite stage overall. It's really fun to route this one and get a lot of items at max value, and Sanae has the best theme in the series. Her boss fight isn't the most fun, though, with most attacks either being too hard or too easy. At least her opening nonspell is extremely fun to dodge.
Stage 6: Also MoF. Another fun stage portion, most of Kanako is tricky but nothing over-the-top, and of course, the stage climaxes with Virtue of Wind God.