As said, so much to do it's not really a chill out kinda place. Having said that, there a plenty of beaches just a short drive away. Miami is nice, but a bit rough. Still recommend it though.
I am going this May (4th time) and we are doing Tampa/Busch Gardens for the first time. We stay on I-Drive as it caters to all things you want on an evening. Food, Bars, Entertainment, etc.
Obviously you should do Disney. You said you are already doing Universal. Best thing for us are the waterparks. Blizzard Beach and Typhoon Lagoon at Disney are great fun. Aquatica waterpark (Seaworld) is brilliant. We're not a massive fan of seaworld itself though.
We went to Key Largo a few years ago to swim with dolphins. It cost around £150 each for the transport, 1 night hotel, swim (1 hour in a river just down from the sea) and a stop in Miami on the way home. Much better value than swimming with them at Discovery Cove which is around the same price for a 10 minute swim. But that depends if you wanna do that. Key Largo was beautiful.
Have fun.
For tickets, the best prices we usually see are;
Disney - £255 (14 days for price of 7)
3 Park ticket - Busch Gardens/Seaworld/Aquatica - £92 (14 days)
Universal we paid for on the day and was around $60