Northeast of Naples - Audubon's Corkscrew Swamp Sanctuary: easily spend a whole day along the substantial board walk; we were there from opening to closing.
Just south of Naples: Rookery Bay National Estuarine Research Reserve, Tower Road, Naples: trails through scrubby brush with deer and at least one massive Diamondback Rattlesnake.
East of Naples along Tamiami Trail:
Ten Thousand Islands NWR: great and easy walk in from the car park with an excellent observation platform. When we were there (March) it was like walking through an open aviary of wetland birds.
Fakahatchee Strand on the north side of Tamiami Trail: great boardwalk into the swamp.
Big Cypress Loop Road, off Tamiami Trail, particularly Gator Hook Strand and Sweetwater Strand
Don't miss Clyde Butcher's Gallery, along Tamiami Trail: great shooting right out front, and very impressive works inside.
There is also the drive north off Tamiami Trail to the training airport; some good ponds there with water birds.
We were there for 7 days, never made it to Everglades NP, yet never ran out of places, nature and wildlife to see and photograph. In fact, the day we tried to go to ENP, the parking was full, so we chose not to wait and discovered a bunch of unlisted ponds and wetlands west along Tamiami Trail.