Thanks. So far our idea is:
Miami Beach upon arrival for maybe 3-4 nights.
The keys for 4-5 nights (key west or another one?)
Everglades for one day (airboat etc)
Then on to the gulf coast: Naples etc
Probably then make our way north and then across, maybe passing Orlando for a short visit to Disney World. But not particularly important to us.
Kennedy space center would be nice.
Most important to us: Sun, beach, relax. Good food. Walkable areas for exploring by foot (at least most of the time).
Ideally we would like to stay 3+ days in most locations (some exceptions with one night are ok). Even more in e.g., a nice beach town.
EDIT: I do have about 5-8 days worth of hotel points at Hyatt. Will want to use those as well for the most expensive / nicest / busiest places and times.
Does this help? Thanks a lot in advance!
Miami Beach I would grab for one night only. Get you're rental, leave early in the morning and head towards the Keys. Take your time down, the drive is beautiful! Grab a place to stay here for the night (plenty of restaurants to choose from). Next day, I would see the Hemingway House and Key West Shipwreck Treasure Museum. Make sure you stop at Cuban Coffee Queen! Best coffee in the Keys and the only time I ever woke up early on vacation to walk two miles to get some.
There's really not much to do in the Keys that don't involve diving/snorkling/fishing/drinking (oh geez...so much drinking!), so I would start heading back, grabbing a room in Key Largo (I stayed at the Hampton Inn and there's a great restaurant across the street) for the night (look for Iguana's in the trees!) and make your way towards the Everglades in the morning.
After having fun in the 'Glades, I would spend some time on the west coast, working your way up to Tampa/St. Pete (I would recommend using Trip Advisor to check out what to do in those areas and get reviews/prices for lodging and food). Then make your way over to the middle of the state for Disney* and any of the other attractions you may be interested in. After Mickey has emptied your pockets ;), head over my way to take in the beaches and the Space Center (that is much more worth it than Disney imo), then head back south for your trip home.
*If you want a small taste of Disney on the cheap, head over to Disney Springs, their shopping mecca. I know, shopping and mustachian don't go together, but there are a number of places for photo-ops with you're little one that are free and it is a nice place to walk around. You can always catch a Disney bus and head over to a monorail hotel (Contemporary) and ride to each hotel to check them out, or catch a bus to Animal Kingdom Lodge (not the park!) to check out the free-roaming animals they have that are part of the Animal Kingdom Park.