There are no beach resorts on the mainland that are really close to the airport, so if that's the priority, then I'd recommend either Ambergris Caye or Caye Caulker. Both are nice but AC is definitely the higher budget destination (more tourists, shops, restaurants, nightlife, etc.). CC is smaller, quieter, lower budget, more laid back, and it attracts more backpackers. I don't know which one you would prefer.
From either caye, you can get an early morning flight or water taxi and make it to the airport on time -- a flight would be the quickest & easiest. Whether you go by flight or water taxi, make sure you buy your tickets a day or two in advance. The water taxi services and both airlines have websites with schedules & fares -- the links are on the BelizeBus site.
If you want to spend your last night on the mainland close to the airport, the D'Nest Inn (B&B style) is nice, and located in a quiet neighbourhood. The owner will probably drive you to the airport? Unfortunately, there's probably not a lot to do there.
Another choice might be the Best Western Belize Biltmore Plaza Hotel on the highway -- it has a swimming pool.