A lot will depend on where you're traveling from. We travel from Colorado.
For us, Bonaire is a little difficult to get good connections to, but the diving is excellent. It's shore diving, unguided, which can be problematic for newish divers. It shouldn't be a deal breaker, though. Most of the dive sites have excellent landmarks, and the lack of significant current makes navigation pretty simple. Worse case, you can use Prairie Dog navigation - pop your head out of the water, see where you are, then drop back down 10-15 feet to get out of the waves while you swim in.
This time of year, connections to Bonaire (for us) are ridiculous; either ridiculously expensive or ridiculously long.
Turks & Caicos and the Bahamas are great diving, but by no means inexpensive. Ever. I posted a review
HERE about diving in Nassau with Stuart Cove's Dive Bahamas. Their price is $125 for a two tank, with very short bottom times and long transport times.
I find Cancun and Cozumel easy to get to and affordable.
Both are boat dive locations, so you will have a guide.
Cancun is shallower (other than a couple wrecks, there really isn't anything deeper than 60') and generally has milder currents. We dive with Alvaro from AlwaysDiving and it costs about $80 for a two tank.
Cozumel is deeper, and generally has more current, but it's still nothing that the average newish diver can't handle. We dive with Aldora Divers and it's about $100 for a two tank, but you can get HP120 tanks for tons of bottom time. Especially since most newish divers tend to go through gas faster.
Both places have AI resorts if you like those (we do...).
Cancun, obviously, has the most night life, for when you're not diving.
Belize can be good, if you get a little lucky. I recently booked a week at Coco Beach Resort for this Janurary at $2200 for the flight and resort. White Sands offers discounts on pre-paid multi-day packages, but their base rate of $80 for a two tank is very reasonable. Belize can also be pricey, if you don't get lucky. Kim booked two days after I did, and for the same trip it's costing her $2000. For one person.
Roaatan and Utila are a nightmare to get connections to, for us.