That would depend on your age and interests. When I moved here, my son and I would take day trips to small towns around the area. I loved Arcadia for all it's antique / collectible shops. We drove to all sorts of flea markets, and found they were pretty much all the same. We picked strawberries in Plant City one year (February is the best month), which was a lot of fun.

We discovered little gems like in our area the Myakkahatchee River state park, which is tiny, but beautiful and secluded. We went walking in Carlton Preserve many times on its well laid out walking trails.

I think the most fun we had was one year coming back from SC when we decided to take 301 home instead of I-75. Going all the way from I-10 to Sarasota on 301 was such a lovely experience. All the small towns, little roadside stands selling produce and boiled peanuts, lovely tree lined streets, historic landmarks galore, and real people in little roadside markets.

Weeki Wachee's mermaids are worth seeing. If you like gardens, there are little gems all over the state tucked away in corners, like Selby Gardens in Sarasota, with one of the premier orchid collections anywhere.

I've always found that the best fun to be had in Florida is away from the coastline and the big cities, off the beaten path. Take to the center of the state, south of Orlando, north of the keys, and there is plenty to see and do that the tourists miss.

Of the larger state parks on my coast, Myakka River State Park is the very best. It's a little bit of a drive to get there, but well worth it, even if you aren't into camping.

For fishing, the Peace River in Punta Gorda can't be beat. It's a beautiful place, non-polluted, and full of crabs and fish. Take the boat to the mouth, and you're in the Gulf of Mexico.

One of the most beautiful beaches anywhere in Florida is at the tip of Anna Maria Island outside of Bradenton. One side of the island is on the gulf, the other on Tampa Bay. You can walk the beach and look at the Sunshine Skyway Bridge in the distance. For shelling, take a drive down past Fort Myers to Sanibel and Captiva Islands.

I haven't explored the east coast too much, but the area around Lake Okeechobee is one of the most beautiful places around, and with hundreds of miles of shoreline, you can find just about anything you want there.

Florida is a beautiful state, once you get into the "real" Florida and away from the snowbird meccas.

I suggest the Myakka River State Park. I love visiting there, and going hiking and
backpacking. It's definitely off the beaten path. There are 39 miles of trails, along with horse and bicycle trails. There are six campgrounds with camp sites for staying overnight. You'll see a variety of wildlife along the trails and enjoy the peaceful Florida countryside. Read more about Myakka River State Park here:

Source: http://www.floridaadventuring.com/myakka-river-state-park.html

I moved to Pinellas which is Tampa, St. Pete, Sarasota, and Clearwater 2 months ago.

Some things that I have found that I love in the area: Ybor City, the Columbian Restaurant, Pier 60, Sunken Gardens, Florida Aquarium...yesterday I saw my first gator at Sawgrass Lake.

The list is huge. The best thing you can do is get a Fromer's travel guide.