I also like playing Yoshi on Battlefield. It's somewhat cramped but it doesn't hinder Yoshi like it does most characters. He can uair through the platforms and the spacing you can get with platform wavelanding is too good. Also, Yoshi can do some pretty sick ladder-type combos up the platforms with uairs/DJC uairs and utilts.
For example, I did this combo on Battlefield (to Link I think). I don't remember exactly how it went but it was something like this (combo is slightly exaggerated lol): bair/utilt/utilt/utilt/DJC uair/utilt/DJC uair/FH double uair *land on next platform*/DJC uair/FH fair *land on next platform*/dsmash kill.
It was pretty hot.
EDIT: Mute City and Kongo Jungle 64 are also great stages for Yoshi. A few people have already stated why Mute is good, and on DK64 you high platforms give you a second recovery option. Also, you can recover through the stage and waveland if necessary. And if you're really in a tight spot the good ol' barrel is there to help you out (or screw you over lol)
EDIT EDIT: You can get some really fast kills on Green Greens too. The fact that Yoshi survives for a long time can really help you here. Blocks (especially bomb blocks) can screw you though. A little trick I like to do is to stand on the blocks, then fall off and uair while falling (this works with any platform though). It's pretty effective because of the blocks' low height (the lower the better) and can kill floaties and lightweights. Dsmash while on the left and right islands can kill at really low percents.
I also like Mushroom Kingdom II (It's not banned here XD) as a Yoshi stage. You don't have to worry abut recovering, and this is another stage where Yoshi can kill very quickly. And your opponent can't camp the sides because you can spam eggs at them. And four edges to ECE on = too good. Also, quick edgehogging on any of the four edges can grant you some quick invincibility in times of need.
And one last thing to think about...Jungle Japes has
SIX edges to instant edgehog on.