Bowser has a few places he loves, and a few places you should avoid in entirety, I've found.
My personal opinion here, but this is how I rank stages for Bowser.
- Lylat Cruise—Lylat is a big pain for a good portion of the cast due to Lylat ledges. That being said, Bowser doesn't care about Lylat ledges thanks to the mobility and control of Whirling Fortress. Flying Slam kills at 90 off any of the Lylat Platforms. Also, the tilting stage works in Bowser's favor a good portion of the time as long as you maintain good stage presence along the lower, as it essentially increases how much of the stage is covered by his moves. Also, since the platforms are so low, even an upward angled ftilt can someone on ledge. Space Bowser is best Bowser, but it still can pose some trouble for him. The first problem is the difficulty of using SHADC increases significantly on tilting stages, which would pose more issue if there were zoney characters that were good on Lylat. Another issue is there are a few other characters that just do far better on Lylat than Bowser does, such as Pikachu, who gains mobility like crazy on Lylat. Therefore it's MU dependent, but more MUs turn in his favor here.
- Battlefield—Bowser can get pretty silly on Battlefield, with Flying Slam sometimes killing at 70 off the top platform. With all the platforms everywhere your punish game gets really nice too. If they airdodge on landing into a platform you get a punish, if they land on a platform without air dodging you get to put out one of Bowser's many lasting hit boxes. If they try shielding on landing, command grab. I love Bowser on platforms, and as such Battlefield treats Bowser really nicely. Simply being on a platform with Bowser pressures them to act in a different way, making them want to stay away from you. Which is great for you, because as long as they aren't packing projectiles for day, this gives you control of the stage until they return to neutral. That being said, just like Lylat, some characters are just so much better at Battlefield than Bowser is. Pikachu is an excellent example, who... gains mobility on Battlefield. Not to the levels of Lylat, but still more than he would on some other stages. Also, Diddy and a bunch of the sword crew opt for Battlefield which is not the best of news. He still does pretty well here, but zoners are more of a problem here than on most of the other stages on this list. This and Duck Hunt are the stages that the Bowz can take advantage of Bowser Bomb onto ledge.
- Town & City—Town & City is a pretty unique stage. Unlike any other stage on this list, it doesn't promote mobility for some characters, it doesn't hinder zoners, your ledge game changes slightly (there's a platform that occasionally chills way above either ledge and some characters will jump from ledge and retreat to it, so you have to be ready for that read occasionally. I personally don't go here often, but I've seen plenty of Bowsers use it to their advantage. Flying Slam kills at lower percents here as well, which is great. Bowser is one of the better characters on this stage, for once, and as such doesn't suffer too much matchup wise here, but there is still stuff to be wary of here. For one, T&C has weird ledges, that sometimes just ignore Bowser's Up-B as well as few other characters. This ends up with us either not grabbing the ledge, going slightly above ledge instead of sweetspotting which we all know hurts our hearts so much, or landing on stage with Up-B which is so damn painful for Bowser. A similar thing phenomena happens on Battlefield Omega. They're just weird ledges. I really am scared of weird ledges, which puts this stage as Bowser's #3.
- Castle Siege—Finally, a stage that hinders zoners. Castle Siege is notorious for how it eats projectiles in it's second transformation. That being said, Flying Slam tends to kill pretty normally here, except during the transformations, which can really work in Bowser's advantage. Also, walk-offs are Bowser's best and worst friends considering Like I mentioned on Lylat, tilted stages increase the difficulty of SHADC, and every singles transformation has a lean, so approaching the hindered zoners, becomes more about shielding rather than this safer approach. No Bowser bombs onto ledge here, unless you know the stage super well. But Bowser's stage control here becomes fantastic in every transformation. One thing to note though: The statues have weird properties against Bowser's more powerful hits, delaying them a good deal, so be careful about doing too much near them. That being said MUs here are scary. Some Diddy players, MVD for example, don't care at all about their projectiles being eaten. Also, against MVD I surprisingly learned that Castle Siege is one of Duck Hunt's best stages, which doesn't seem to make sense, until you actually play him on it. He gets way more options here, which is super strange. Play smart on Castle Siege and it'll treat you really nicely.
- Duck Hunt—This stage I've been working on mastering as a Bowser stage for a while now. It's great for dealing with some characters but not as great for dealing with others. It's similar to the way that Town & City is a mostly flat stage that gives Bowser some more Flying Slam kill potential. However, the "platforms" on Duck Hunt are super tiny, so they are not reliable for landing, just a forewarning. Also, the ducks hinder zoners, which Bowser likes quite a bit. The walls tend to make Bowser's recovery more predictable than on other stages on this list. Also, there pixels in the dirt which make bowser bombing onto ledge super easy.
All of this considered, MUs heavily influence your stage pick for Bowser, like Zigsta mentioned. There are also a few things I didn't mention about stages. For example, I will always ban Delfino with Bowser, but I'm sure Zigsta would prefer to go there being a Brawl player. Brawl players have an unnatural affinity for Delfino, that makes it dangerous for those of us that aren't Brawl players to consider. I know this sounds super silly, but this is something that playing against so many high-level Brawl players in my scene have confirmed. I personally ban it because the extremely low ceiling during transformations paired with the Bowz being combo food making for ugly matches (Diddy can kill with an upair at about 45 :L). As such, consider your own affinity for stages before blindly going to a certain stage.
Another thing, there are stages that you should just avoid with Bowser. If you play Doubles, Kongo Jungle 64 should be one of your immediate bans on counter pick. Your recovery is sometime just completely ignored by the ledge, and it happens often at that. For singles, avoid Battlefield Omega. It will also mess with your recovery due to weird ledges, and it doesn't have the advantages that Town and City gives you. I'm sure I'm forgetting some things, but this is all that I consider when I'm choosing a stage for the Bowz. I apologize for the long article, and I hope this helps!