You didn't say what part of the country you were interested in, but you can get pretty much everything you are looking for at
Blythe Island Regional Park and Campground in Brunswick, GA. They have a small catch and release lake and the park borders the South Brunswick River. There is an archery range within the park and there are hiking and biking trails in the park.
The park is a county run park with a State Park feel. Sites are semi private. The park is less than 30 minutes to Jekyll Island with a lot more hiking and biking trails as well as fishing piers and a lot of history. St. Simons Island is just north of Jekyll Island with lots of good restaurants. Both Islands have plenty of Public Access to the beaches of the Atlantic Ocean.
Winter temperatures aren't as warm as Florida. It does sometimes get below freezing at night. February is usually the coldest month with a few nights with temperatures in the upper twenties. This winter we did not have a hard freeze and we only had a few nights with temps below freezing.
Brunswick is about 1 hour south of Savannah, GA and 1 hour north of Jacksonville, FL, so there is plenty to see and do in 1 day without making over night excursions.
-Michael
