There are a number of nearby beaches and everyone has different favorites. You're going to have to drive 45 minutes to an hour to get to the beach, though (depending on where you're staying)... so be prepared for that. Boca Grande is BEAUTIFUL, but it has strong currents and a reputation for sharks, so not the best option for kids. I like Blind Pass Beach (a.k.a. "middle beach") on Manasota Key for family beach days.
Also, for a different sort of beach trip, Caspersen Beach in Venice has TONS of shark teeth. You'll find them on Manasota Key, but there seem to be more on Casperson. It's a bit rocky for a "beach day" (at least in my mind), but it's a great place to go for a few hours to sift through the sand. (You can buy sifters on a long handle, or just use a colander.)
Charlotte Harbor Environmental Center (as recommended by LifeHappens) has nice trails and a visitor center with exhibits that kids might enjoy. If you don't mind driving a bit further, my two favorite nearby hiking trails are Myakkahatchee Creek Environmental Park (North Port) and Sleeping Turtles North (Venice). If you go to Sleeping Turtles, Snook Haven restaurant is a fun lunch spot on a weekday. (It's crazy on weekends.) It's definitely touristy, but in a fun Old Florida way.
In Port Charlotte, Ollie's Pond tends to have good birding year-round. It's a 1-1.5 mile walk that's surrounded by a residential neighborhood, but the pond attracts lots of birds.
Make sure you go to Myakka River State Park while you're in the area, if you haven't been there before. It's up near Sarasota, but totally worth the drive.
Punta Gorda tends to have a fair number of art festivals, depending on when you're coming. Some are good, some are meh.
If you don't mind driving up to Sarasota for a day, I can't recommend the Ringling Museum enough. There's a circus museum, John Ringling's mansion, and an art museum... all set in a beautiful spot along Sarasota Bay. It's a really nice daytrip.
