If you want a true Miami experience, I would not stay near the airport. We stayed 2 nights near the airport at an Embassy Suites once pre-cruise and there was nothing in walking distance except a terrible chain restaurant Bennigans. We spent more on cab rides to and from the beach than we did on our hotel room. If you are looking for a reasonably priced, good location on South Beach, you may want to check out the Winter Haven. I have not personally stayed there but I would based on a recommendation of a close family member. Rooms are smaller and not directly on the beach but a central location in South Beach.
If you just want a decent place to stay with breakfast and airport shuttles, I do recommend the Embassy Suites as a layover hotel.
I have heard South Beach is the way to go if you want to go out. We ended up in a little airport hotel that looks clean, has free breakfast and an airport shuttle. My husband apparantly has no interest in florida, lol! He just wants to sleep, get back on the plane and then run to the beach once we arrive. Thanks for all the good info. This board is amazing!!