I can't speak for Belize, but Grand Cayman would work. I can only recall one shopping center(strip mall) in Georgetown that had a flight of stairs to go up, most of the others were on the ground level. A couple have back entrances at street level from the parking lot and a few steps in front. There's sidewalks in Georgetown - dodging thousands of cruise ship tourists during the day will be the bigger problem.
As I recall there's also sidewalks along most(all?) parts of Seven Mile Beach where there's any kind of commercial development. Most of the restaurants are near/in strip malls so at most there'd be a couple steps up to a patio. The only place that I can recall going up a lot of stairs was the Hard Rock, but they may have an elevator too.
Not that you necessarily want to stay there, but the Hyatt is fully ADA compliant. Also Comfort Suites has elevators. Most of the private condos along SMB are on ground level also.
Some areas of Cayman, like Sunset House are downhill to the water. But there's a driveway and ramps down to the water's edge. And the restaurant (and MyBar!!) there is accessible. Probably the only place you couldn't go with mom is the Cathy Church gallery, it's down a flight of narrow stairs and kind of tight inside. I wouldn't stay there though, it's a diver's type of place, not much else to do in that area.
I wouldn't do Bonaire, I can't recall any of the resorts that had completely paved walkways - we saw a lot of them. The North resorts are high above the water so there's steep ramps at some of them. The exception would be Sand Dollar or maybe Buddy's. Downtown would be fine, there's wide sidewalks and the promenade along the waterfront. Condos to the south are mostly perched on small cliffs with stairs between levels. We stay at BelMar, but they have a 15' drop to the water just off their pool area - no fences. And unless you get a groundfloor unit, it's all narrow, twisting stairs. The exception in the south might be the Plaza, the resort, pool and restaurant have easy access.
hth,