My wife goes every summer for work (archaeology) and I visit occasionally while she's there.
Belize City is pretty sketchy, but you need to go through it to get from the airport to anywhere else.
Recommend staying out on the cayes for the island getaway experience. Ambergris Caye is much more touristy/resorty with beaches and nicer accommodations. Caye Caulker is quieter with less luxury but IMO it's the better experience. You can stay in a hotel (usually pretty small, like only 8-12 units) or you can rent a cabin/cabaña. You can do a half-day trip to go snorkeling or fishing off the coast.
Inland, Belize is not very big but the road network isn't great, so it takes awhile to get anywhere. Definitely recommend checking out the Maya ruins (where my wife works). Belize is also pretty close to Guatemala (highly recommend Flores/Tikal) and Cancun/Yucatan, so you can make it a bigger trip if you want.
You do have to be a little careful as some of the locals will target ostensibly wealthy white tourists, so I'd advise against flashy jewelry and such and just maintain a low profile while you're there.