Final Destination is a great stage for him, but it all depends on his opponent. If you're up against a spammer/camper/chain-grabber, then you might be having some trouble. If not, then you should be okay. Nothing will interupt your chaingrabs unless there's an item in the way.
Smashville is a great stage for Yoshi. Like Burntsocks said, it helps with our aerial/platform camping and we can get some easy hits with our u-air if our opponent likes to be on the platform. It's a smaller version of Final Destination, and it's one of the few stages in which Yoshi can travel under the main platform from one side to the other.
Yoshi's Island is a very good stage for Yoshi. The shy guys are barely a nuisance, so you shouldn't worry about them that much. Although the slanted ends might mess up our chaingrabs, they allow us to auto-cancel our ground pound so we can grab the edges, and that's a great set-up for ECE. Personally, it's my second-favorite stage in the whole game. I just love the songs and the visuals.
Battlefield is a pretty good stage for Yoshi. The main problem is that the small platforms interfere with our chaingrab, and having a platform interrupt your ground pound is something that you don't want to happen. Other than that, Yoshi can have alot of fun moving from platform to platform because of his excellent air movement, and using u-air on his opponents should be fairly easy with all the platforms around. This is another stage in which Yoshi can travel under the main platform from one side to the other.
I think the best counterpicks for the Yoshi are the ones that allow him to come from under the stage, i.e. Delphino Plaza, Halberd, and Norfair. Of course, those are just my personal favorites.