Alligator Bayou (also near Dixie Landin') has swamp tours. There is also the Bluebonnet Swamp. Dixie Landin' has a haunted house that is open on the weekends, along with the rides. I heard it was $10, but can't confirm that.
You should go eat pizza at the Pasttime Lounge. Also go get breakfast at the Silver Moon on chimes st.
KY tiger there is a KOA campground in Denham Springs that is real nice and is about 10 minutes from LSU via the interstate. If you get a chance you might want to take a walk through LSU's campus and show your children the Indian mounds(kids are fascinated by them) and tell them about the battles that were fought during the civil war on a plantation that that is now the campus of LSU. Besides the above mentioned places and those of the other posts, Baton Rouges biggest asset is the people! Go to a restaurant or a park, or even a grocery store and start a conversation, you'll see what I mean, BR is the biggest little town I've ever seen. Hope you enjoy your stay!
I had been going to Alligator Bayou ever since the 70's. It was a great place nearby to go to Spanish Lake to catch some bream or sac-a-lait or to go duck hunting. Now they have turned it into a "tourist attraction" They don't allow shooting there anymore and a couple of years ago my brother went there prepared to launch his boat at the landing about 4PM one July afternoon. The people who run the boat launch told him that if he was not back by 6 PM that they would lock the entrance gates to the boat landing area and if he wanted to get out it would cost him $100 to get them to unlock the gates. We used to go out there all the time on summer afternoons and fish until dark and head home at 9PM or later. Well, thats progress for you.
