Go to Key Largo. Try SILENT WORLD dive shop at 103.3 mile marker (shop is at 103 & dock where boat leaves from is at 106). They have a 5 trip package for $179 plus tax. Check out their web site. We used them in May and they were good & great price.
As far as where to stay, you have about 3 different choices. You have the "Key's Style" places (not fancy but cheap and reasonable clean), the chain hotels like Holiday Inn (Mile Marker 100)(about $150 a night) and then the "luxury" places such as condos like Ocean Pointe Suites (about 90 Mile Marker)(also have a web site). Every place in Keys goes by Mile Marker, since there is only 1 main road. 107 at top of Key Largo down to 0 at Key West.
Diving varies from easy reefs to more advanced wrecks. I suggest SPIEGEL GROVE - an awesome wreck that you can luck out on and have little to no current, making it an "easy" dive at 55 feet to the side of the ship; 100 feet to mid line; & 130's to the sand. If you feel like a "challenge" try the Duane or Bibb. They USUALLY have a strong current on them. It is possible to luck out with little current, but normally you are hanging off the decent line like a flag in a stiff breeze. Not uncommon to see divers miss/lose the line and drift off toward Miami. Definitely not for the faint of heart or less skilled diver!
Have fun!
Mike