Ok, I have done 5 annual trips to the keys. Here is how I go for cheap.
First, fly into Ft. Lauderdale not Miami. FLL is cheaper and only a 30 min longer drive. Fly Southwest or Air Tran. Make sure you check prices carefully. A lower airtran price may not be the best deal. Airtran charges for bags Southwest doesn;t.
Rental car: Shop around drastically. I just booked an Enterprise van for $280 for a week. Everyone else was in the 400 range. Check the off airport locations. These will usually be cheaper then the airport location and they will pick you up at the airport for free. Bring your own GPS in your carry on. Do not rent theirs. Also, Check your regular car insurance it will probably cover your rental. Check to see if the the rental car place offers prepaid gas. Get this if you don't plan to drive to far and only if the rate is within 2 cents a gallon difference. This will save time on the way back to the airport. Also check BJ, costco and others for discounts on the rental car.
Diving/hotel: First narrow down where you want to go. I recommend Key largo for what you want. If you stay at the Key Largo marina you have several hotel and dive shop locations that you can walk to in one minute and not have to waste gas.
Hotels- Marina Del Mar, Holiday Inn, Ramada Inn and Suites at Key Largo. My recomendation for you is Ramada. It is usually the cheapest and they have a good free continental breakfast. Plus these hotels are owned by the same parent company. You can use the better Holiday Inn pools with no problems. I recommend trying to negociate a rate with Ramada before booking diving. Get that rate and compare to what the dive shop package rates are. Choose the cheaper price.
Diving: Of the top of my head there are several operators at this marina. Some of the larger operators are. Rainbow Reef (free dive guide), horizon divers, Ocean Divers. All of these offer package deals. I prefer Rainbow Reef because of the free guide. I like it because I do photo/video and don;t want to worry about fidning the boat. I kow that you are an instructor but this is a value that is free. Most places offer more you dive the cheaper it is per dive.
If you dive on Fri, Sat, Sun. This is what I recommend. Am/PM on Fri do shallow reefs on air to max you bottom time. Sat AM/PM trips This time try and go the Benwood wreck. It is a partially intact wreck and shallow. Lot of bottom time and tons of fish. Do a night dive this night. Sun do a AM/PM trip again. By my calculations this will give you 13 dives. This will put you in the 60 to 65 dollar range for a 2 tank dive with weights and air. That is cheap. Also by staying shallow you get max bottom time which equalls more dive for the money.
Food: Eat the free it breakfast it is good and good variety. Sharkeys is in the marina and has fantastic food. It is about the same price as a TGI Fridays. There is a Wendys accross the street. These are three choices that don;t require you to waste money on gas.
A little research goes a long long way. This can be done for a very good price. The keys are awesome. hope this helps good luck.