Dutchjet did a very good job of summarizing it. I can add to what he gave you a list of most of the cities they served.
Miami, PBI, MCO, Daytona Beach, FLL, JAX, PEN, TLH, TPA, MSY (Air Florida Commuter only), Ocala, Key West, Freeport, North Eleuthra (with 737's), Grand Turk, Santo Domingo (from MIA and at one point JFK nonstop), Port Au Prince, Puerto Plata, San Salvadore, Tegucigalpa, San Jose (Costa Rica), Panama City (authority but never operated), Marathon, STT, STX, Montego Bay, Kingston, Cozumel (charters), Las Vegas (charters only from MSP), Georgetown, Gainesville, Treasure Cay, Marsh Harobour, Rock Sound, Belize, San Pedro, DCA, IAD, PHL, HPN, BOS, TOL, ORD, MDW, EWR, LGA, JFK, ISP (very briefly and I don't believe it was ever published), CHS, SAV, DFW, Houston, Burlington VT, Cancun (charter only), Mazatlan (charter only), Zihuatanejo (charter only), Shannon, London, Brussels, Amsterdam, Zurich, Tel Aviv, Madrid, Dusseldorf, Frankfurt (charter only), Oslo, Stockholm, Bermuda, Naples, Fort Myers, Quebec City (charters), Cincinatti, Cleveland, Columbus, Detroit, Indianapolis.....pretty impressive system!
By 1984, they were in major financial straits and the guy in charge of sheduling started opening new routes to just about anywhere to make some money. I know they were supposed to operate from Long Beach to LAX (with no link to the east coast) and from Pensacola to Denver. Again I am not sure if they ever got these routes up and running. The MIA-MAD and MIA-LGW routes went to Eastern. At the end Midway only ended up with seven 737's and a few routes from MDW to Florida as well as nonstops from IND and DTW to Orlando. They also operated HPN to DCA and from MIA to TPA, MCO, STT, and STX and from PBI to TPA. Midway also took over Air Florida's repair station in MIA.