That is an absurd drive. I hope you have a nice newish car and plenty of money for gas.
As for the destination - keep in mind that from miami to key west can take anywhere from 2.5 to 5 hours depending on traffic. And for getting there - you'll probably want to head down I-95 south in florida, *until* you get to a point where you can get on the Florida Turnpike instead. Once you get on the FL Turnpike, don't get off it (unless you want to do some sightseeing). You can get on the turnpike somewhere around Orlando, and stay on it all the way down to the end of FL. Once you're there, there are clear signs that will direct you to key west. Tolls on the turnpike for the whole way might end up costing you about $20, but it is definitely worth it since you will avoid a lot of commuter / in town traffic between palm beach and miami.
Edit: There is nothing to see when you're on the turnpike, but nothing to see when you're on I-95 either. If you're looking for touristy destinations, you could swing off in West Palm Beach, Ft. Lauderdale, or Miami. (check out south beach) But none of them will be a "quick" detour, and really there's no scenic drive down - any drive with scenery would EASILY take twice as long, if not longer. I once drove from West Palm to Ft Lauderdale... on A1A (the road along the beach). A1A time? 3 hours. I-95 time? 45 mins.