I've dove with Conch Republic, Blue Waters, Silent World, and Rainbow Reef divers. IMO there are more good DiveOps in the Keys vs. bad...
Silent world is north, and they do some spots that the others don't (like City of Washington). They maybe the least expensive option. I believe they also can setup accommodations.
Blue Waters is at mile marker 100. They are a small Op, but they have a very comfortable boat, maybe around 30'. They limit the divers to 10 which is not crowded. Brent and Capt. Marvel run a good OP.
Rainbow reef is kinda a Cattle op, but they are cheapish if you need to dive in a pinch. They will do deeper wrecks, but expect two dives on Molasses or French Reef as the norm. They are my last minute DiveOp, and I've done several unplanned trips when I was TRYING to drive out of the Keys, and realized I could hit the reefs that last time. They supply Dive Guides at no charge.
Conch Republic is in Tavernier which is at MM 90, so a bit south of Key Largo. They do some dives like Conch Wall that some of the other ops north generally don't like to go to. Brenda and Gary run a great op, and they have two boats and frequently do the deep wrecks.
Most of these diveOps offer multi day discounts, so you may want to choose one for that reason.
We have stayed at Ocean Pointe ~ very nice Condo's, mid priced at around $150 per night, but they come with amenities one would expect with a condo. Some deals can be had, and I think Brenda or Gary would be the folks to contact for a good price.
Brent set us up one year for a night at the Marina Del Mar. It's on the low side at maybe $75 a night. The rooms are a bit dated, but clean and comfortable. The pool is nice, and this is walking distance to any dive op around MM 100 like Blue Water, and there are a few.
If you are not picky, and want a cheap place to stay, try the Sunset inn in Tavernier. At rooms starting at $50 per night (weekdays), and efficiencies with a kitchen at about $65, this is a bargin. Rooms are dated, but they are clean. The pool is also clean, and well kept. We run into a lot of FL locals when we stay there.
SpearGirl will likely reply to this thread as she manages some condos around Tavernier I believe. I've not used her, but others have, and I believe her prices are good.
The diving in FL is good all over really. You may want to spend a couple days on the east coast anywhere from Jupiter, to Ft. Lauderdale, and do some dives at Jupiter, or Boynton, or Ft. Lauderdale. Those dives tend to be drift, but can be a blast.
Have fun, and good luck.