Look at Cozumel. You can get there in around 6-8 hrs. on AA connecting thru DFW for $600ish. There's about 6 hostels downtown starting at $13 and a lot of sub-$50/nt rooms. This one looks like an option:
Agave Azul Cozumel Hotel & Diving (Cozumel, Mexico) | Expedia
My friends (divers) stay at Villa Blanca. There's 2-3 dive shops either on premises or within a block or two. It's not in town though - a couple miles south - so factor in a cab which I understand can be pricier. Also I think nearby food options are limited.
Villablanca | Cozumel Mexico
Dive Paradise bundles with them also. 4nt. packages are around $500 diving/room.
Villablanca Garden Beach Hotel - Dive Paradise
Carnival in Cozumel is sometime in February also so that may affect the rates depending on when you go.
fwiw, I've never been there - it was just the first place I thought of that meets your needs.
Roatan has a hostel also - Chillies - same people own Native Sons Diving. Actually Roatan also has plenty of decent accommodations under $50. In the West End you won't need a car - a cab from the airport is fixed at $25 and there's a water taxi or local cabs. Also a small food store and truck vendors but food is really cheap there. Food is everything from street vendors to the finest Indian cuisine in Honduras.
And diving is 10/$350 from 1/2 dozen shops. Most of the shops have their boats in the harbor out front. We liked Coconut Tree but Native Sons, Reef Gliders, West End Divers also get good reviews. This gives a good overview of options in that area.
Coconut Tree Divers - Roatan
Flights are longer - close to 11 hrs. with an early morning layover of about 5 hrs in Houston. Same price though. Since you've been to Belize, I suspect the diving is sort of similar since they're so close.
Maybe price Maui?. From LAX it's 5-6 hrs. each way - we often fly thru there now.
There's a Tiki Hostel in Lahaina that's near the harbor where two shops keep their boats. On Front St. which is where all the restaurants, nightlife etc. are.
Tiki Hale - Newest Hostel in Lahaina, Maui
Diving is pricier there though - 2 tanks exceed $129 or more.
Reservations | Scuba Dive Molokini, Maui, Lanai, and Hammerhead Shark Diving
If you could find somebody to buddy with - and transportation - shore diving is an option there also. The issue with shore diving with a nearby shop is they're not much cheaper than boat dives although some offer pickup and shuttle to nearby sites. Tank rentals otoh are like $10/day and Maui Dive Shop has $5 fills. A cheap small car to get around will be cheaper than a cab from the airport. Book in advance - walk-ups are about 150% higher on arrival.
Maui in February is peak season though so maybe more expensive.