I like Falcon on Mute City, actually. He's probably the only character I'd take there, if only for road comboing, a nice place to DI, and a much more exploitable recovery.
Dream Land 64's also nice in general, but only for your own survival. Kinda hampers your own killing ability, but with Bowser's edgeguarding, it isn't that big of a deal, in my opinion.
Yoshi's Story is known for being "Bowser's level", and for good reason. Easy Fortresshogging, and small blast lines make this place ideal for Bowser's KOing strength. There isn't a lot of room to move around, which is a curse as well as a blessing, given Bowser's size. Sometimes the curse is more than the blessing (It's Marth/Ganon's Story, in my opinion), but other than that, it's normally your best bet. Most people will ban it against a good Bowser player if given the chance.
Green Greens is very fun, and very abusable, but the same can be said for characters that destroy on Yoshi's Story. Much of the same can be said. It'll just end up being a battle for the low ground. Bombs are fun to run into with an opponent nearby, since Bowser isn't sent as far.
Fountain of Dreams is necessary against a chaingrabbing Sheik; the platforms are as good a defense as you're ever going to get (which, incidentally, isn't much in that matchup, period). Its shape is similar to that of Yoshi's Story, but there's more room and variability. Take that as you will, depending on the matchup.
I started banning Final Destination; I feel that Bowser does his best with platforms, mostly for mindgames and maneuverability. Fortresslanding (I don't know if that's what it's actually called) is nice, too. They can also be used for easier techchasing, which is nice. Or maybe I just hate shorthop gayzers from Falco...
Although I'm kind of inclined to counterpick Brinstar, if only for the "epic legend" of "the Lava Combo" that is thrown around in the Southeast because of one of my tournament matches...it's now a crew staple. ;/
(Don't take the last bit to heart; I haven't analyzed the stage well enough to give good judgment on that. I just like hearing "get 'em in the Lava Combo". ^^; )