Done that in the past - as above, no real sights on route to be honest.
You can take the T'pike towards the coast from Orlando, and the drive is through the towns like West Palm Beah, Pompano, Ft Lauderdale, but this is a drag and loads of traffic. You might prefer 27 or 441 - takes you around Lake Okeechobee and then south through some real empty 'old Florida' and the farming areas to meet H. 1, south of Miami. Miami to Key West is about 130 miles.
There really aren't many tourist facilities other than small towns with maybe some fishing, or air boat tours through some swamps. Might be an alligator park or two to see though.. so if you want the drive to be a 3 day event, maybe go to the coast and take your pick...
http://www.visitflorida.com is a link to a useful site for visitor click on the areas for details for towns and attractions to see.
One nice stop over in the Keys is at the John Pennekamp Sate Park - nice beaches, coral reef, mangrove walks, snorkelling and yacht cruises.
Key Largo is pleasant too - and you get gravy with your KFC's.!!... - and there are a number of other parks and refuges as you go through the Keys before Key West itself. The Highway 1 drive over the bridges is worth the effort on its own anyway, so that is part of the attraction. Once in the keys, there are loads of really good accommodation, and cheap if you stay away from the main streets.
Might be worth looking at Google Earth if you haven't already. This will let you see the route and the road numbers to follow. - make sure the 'roads' button is ticked for them to show. Dead easy to get an idea of the place.
Have a good break..