Icies best stages: FD, FoD, Yoshi's (in order)
Final Destination - It's flat and gives Icies a lot of space to WD around. Icies can abuse their horizontal movement here more than any other character, maybe with the exception of Luigi.
Fountain of Dreams - The platforms and blastzones are really nice. The platforms make combos and chaingrabs easy, and the high ceiling makes it hard to die off the top and bottom. Icies F-smash + Side blastzones = Amazing.
Yoshi's - Platforms are perfect for handoffs and combos, but the close blastzones can make this stage troublesome against some characters. If you are against a Marth and have two bans, I suggest banning Battlefield then Yoshi's. Marth is much more of a problem on Battlefield than Yoshis with the top platform being so high and the mid platforms so low.
Dreamland 64 - Huge blastzones can make some matchups extremely hard, like Jigglypuff and Peach (if it wasn't hard enough QAQ) but it can also ensure Icies can recover. While the platforms may be to high to really get combos on, controlling the floor and abusing your moment on the ground is key for a win.
Pokemon Stadium - Minus most of the transformations, Pokemon can be an okay stage for the Icies in some MUs against characters that don't kill off the top, like Peach or Falco. Never take a Fox here. He will hurt you.
Kongo Jungle - Usually banned in some tournaments but it's still worth mentioning. It's got nice blastzones and the 2nd highest ceiling in the game. If you can master the timings of the barrel and use the stage's underside with the lack of collision to recover, Icies can be unstoppable here. Spacies do like to camp on this stage though.
Battlefield - Ledges are bad. Platforms are bad. Low ceiling is bad. Battlefield is not a neutral stage for Icies. Even though they can get combos off the platforms, the stage can really hurt them. Sure, it's bad for a lot of other characters, notably Fox and Falco (I honestly think this is Fox's only bad stage, maybe other than FoD. Spacies have to hold away when illusioning when they try to sweetspot the ledge or they will get battlefielded) but it might be worse for Icies.
Against Sheik, ALWAYS BAN BATTLEFIELD.
If Nana is anywhere near the ledge and get's hit off while she's on her own, she will always battlefield herself. Beware the needles, Sheik can do this easily.
-----
MU basics, generally:
Fox's Favorite Stage: Pokemon Stadium
Where to go against Fox: Battlefield - Fox can have a hard time recovering here against a lot of characters and the stage can kill him a lot. Be careful not to die off the top and you should be fine going to this stage in most occasions against Fox. If this doesn't work try Dreamland. Fox can get combos there too though. Pretty much every stage in this game is good for Fox.
Falco's Favorite Stage: Yoshis - anywhere with platforms.
Where to go against Falco: Final Destination - Falco can't abuse all his aerials and get platform combos on you. If FD is banned, go to Pokemon Stadium. It's your next best bet. Dreamland is good too, but Falco can combo off the platforms a lot.
Sheik's Favorite Stage: Battlefield - loves off stage gimps.
Where to go against Sheik: Dreamland - The body of the stage makes gimps a little harder and Sheik's hard to master recovery can be negated when most other characters can get back to the stage before her and easily edge guard the edges. Yoshi's is great against Sheik too, especially if you want easy-chain grab style points. :3
Jigglypuff's Favorite Stage: Dreamland - loves huge blastzones. Jiggs will always be able to recover unless she hits a blastzone and dies.
Where to go against Jigglypuff: Yoshi's - Jiggs can't float out and get kills like on Dreamland and FD and has to work a lot harder to survive hard hitting moves. If Jiggs bans Yoshi's go to FoD and focus on horizontal kills and not vertical kills.
Peach's Favorite Stage: Dreamland - loves huge blastzones. Peach can be a TANK on this stage if you can't kill her early.
Where to go against Peach: Yoshi's - Peach can't float out and get kills like on Battlefield and FD and has to work a lot harder. If Peach bans Yoshi's go to FoD and focus on horizontal kills.
Falcon's Favorite Stage: Dreamland - Falcon can combo off the platforms and can also mix up his recovery easily. The large blastzones make it easy for him to Falcon kick and get his double jump back.
Where to go against Falcon: Yoshi's - This restricts Falcon's horizontal mobility a bit and depletes his recovery options. Though he can wall jump, he will die early both off the sides and bottom.
Marth's Favorite Stage: Yoshi's, even though Battlefield is better - Marth loves small blastzones.
Where to go against Marth: Dreamland - It's huge and Marth's sword can't go through the platforms!