...would really like to go on a dedicated "dive trip" with a group where the focus is on the destination and multiple dives...
Sounds like you & I share a preference. Okay, realizing I'll hit on some of the same info. as Diver Steve, I'll tell you how I consider options for that.
1.) Bonaire - 7 day stay, Buddy Dive Resort is a fine choice, nitrox likely included & breakfast buffet at Buddy's, figure around 6 days of diving, 4 shore dives/day, & a few night dives on the house reef, you could be looking at 18 to 24 dives, a bit more if you pour it on. Been to Bonaire 8 times. Bonaire is out of the hurricane belt & usually a fine, warm water choice all year long. Not much big stuff except tarpon and a few barracuda, occasional big green moray or cubera snapper. I haven't seen a shark there.
2.) CocoView in Roatan - following up DiverSteve's post, from what I understand 2 1-tank boat trips, drop off on the way back to get 2 more dives swimming back to the resort, plus there's a nice house reef with the wreck of the
Prince Albert for evening & night dive options. In Roatan where you stay will make a much bigger difference in how you dive than is true in Bonaire, from what I've read. Haven't been to Roatan yet. Roatan has a rainy season and can be impacted by hurricane season, so consider the time of year you travel. I'm told Roatan has lush reefs and lots of small stuff, not a lot of big stuff, but read some review threads for more since I'm also told Roatan's underwater habitat varies a lot by which section of the island you dive.
3.) Key Largo, Florida. Dove with Rainbow Reef Dive Center, at the end of the Courtyard Marriott parking lot (where I stayed). 2 2-tank boat dives/day, can do all shallow reef or morning deep dives & afternoon reef, crammed 20 dives into 5 days, cost me $600 for diving + tax & tips. And they put a couple of guides in the water at no added charge. I found Key Largo fishier than places I'd been in the Caribbean. 1 Trip, enjoyed it. Sea conditions vary with time of year and the water can get chilly in winter. I dove with no wet suit September 2013. I saw big barracuda, black grouper, a number of green morays, a few reef sharks and nurse sharks, and on deep wreck dives goliath grouper.
4.) Cozumel - tends toward 2 tank boat dives, from what I understand, but check to see which op.s might offer a 3 dive/day option. And some op.s, like Living Underwater and Aldora, offer 120 cf steel tanks, so you can get longer dives even if you're not doing more dives. There's a recent thread comparing those 2 op.s. On a cruise ship stop I did 2 dives with Living Underwater and my little group was very pleased with them. Weather can be a factor (on another cruise stop, we had 2 dives cancelled because Caleta Harbor closed while we were standing in the dive boat about to go out). I think my 2 dives were in January and the water was around 76 degrees. Known for some big stuff; I saw a big black grouper and big eagle ray, both close up.
5.) Blackbeard's live-aboard in the Bahama's. Often described as 'camping at sea,' the reviews I've read could be summarized as a lot of diving, basic accommodations but good food, around $1,000 + tips and be mindful that's room, board & traveling around site to site. For value, I can hardly imagine a better deal in this region. But read up on the reviews. And the Bahama's water, like the Florida Keys, gets chilly in winter, so if you like diving without a wetsuit, you'll need to time that by time of year. I've not done a live-aboard as yet - being stuck on a boat for most of a week isn't appealing to many non-divers, and for people prone to sea sickness like my wife & main dive buddy both, it's a hard sell. The Bahamas is famous for shark feed diving; figure you'll get a chance to do a group dive surrounded by reef sharks in the area (confirm if this is important to you). Last I checked airfare to the Bahamas for me was not bad!
6.) AquaCat live-aboard is owned by the same people who own Blackbeard's, but costs closer to $2,400 + tips but from what I understand you get a substantially nicer living experience while you're on the boat. Before you decide to go budget, read some reviews. Seems to me the AquaCat tends to get glowing reviews.
7.) Belize live-aboards seem to get discussed often and I'm told Belize is best dove by live-aboard, although there's enough land action (e.g.: Mayan ruins, jungle, etc...) so planning some land time in addition can be worth your while, if you can stay 2 weeks instead of one. Belize is far enough south it ought to be fairly warm water all year; check because you may have a different idea of what is warm. The main reason I'd consider a Belize live-aboard over a Bahamas live-aboard is because some of the trip reports of Bahamas diving have been, well, decent to good but I'd want to know if Belize would be better.
There are a lot of other options, but I believe those I listed are the most commonly discussed mainstream Florida/Caribbean high dive count destinations that more people do, and get to earlier in their dive careers when operating out of the east & central U.S. I figure these destinations are consistently well-known & popular for good reason, and a good starting point. Perhaps someday if I'm blessed to get more seasoned I might consider a live-aboard to the Turks and Caicos, the long (& for me it would be miserable) travel times round trip to the Philippines, etc...
I look at things from a middle class perspective where 1 week is the maximum time off from work and the trip should be under $3,000 per person, or $4,000 solo, including airfare & all expenses, and I don't like flights over 4 hours and travel times over a day total. The scuba equivalent of Walmart or a Honda Accord, not Macy's or a corvette, but not a thrift shop or a moped, either.
If you are rich, have scads of free time & don't mind your butt growing roots into an airplane seat, perhaps someone else can tell you about Wakatobi. In fact, if you're not real rich but don't mind long travel times & have the time, then others can talk about Red Sea live-aboards & the Philippines.
Richard.