Eric,
Like selfbow said the fishing around here is fantastic. I live in Cocoa along the Indian River, always plenty of trout, redfish, snook, and others available. Plenty of offshore fishing available out of Port Canaveral if you want it. The St. Johns River is also right here, great fresh water fishing. More types of fishing than most can even handle.
I'm not real into fishing these days, but there is a local fly fishing club with lots of members. Alligatordond lives in Melbourne across river from Satellite Beach, avid fly fisherman, believe he is Pres. of the club. They probably do excursions to the Keys and other areas.
There are plenty of areas to hunt, some are quota only, some are open without quota permits. As of now we're still allowed a 2 per day limit for deer, no limit for hogs. If you plan to hunt the season when you move here you'll need to apply for quota permits in May or June, if you get in touch before that time I can tell you about the areas near by which are quota only so you can decide which you'd like to try. We are also on a guest permit system at this time. If you get down and weren't able to draw a permit, if I drew I'd be happy to take you along as a guest, then you'd get to hunt and learn the areas.
Hogs are year round on private property and in areas other then WMAs, can be tricky if your not certain where you are. But there are also a lot of inexpensive private ranches which will allow hog hunting. Some for a trespass fee, some charge per hog, some daily hunt fee plus per hog.
I've been hunting and fishing this area since 1965. I have access to (private) hog hunting property, some of which also has deer and turkey. Let me know when your coming, be glad to help you learn the area. Most of the best Osceola turkey hunting in the State is within a 1 to 2 hour drive of Satellite Beach.
Hunting this area of Florida is nothing like hunting out West. Marsh, swamps, Cypress heads, Pine forests, hardwood hammocks, palmetto thickets. A lot of thick dense woods, some visitors can't believe we can even hunt some of these areas. It's definitely different, but you'll learn to love it!