There is an area with ancient oak trees on Live Oak Road there.

You might check out the Cajun swamp tours in Acadiana Park area.

Then you have the Atchafalya swamps and bayous to the east of Lafayette. I'll bet the fishing in some spots is great. Even if you don't like fishing, you might enjoy just getting out on a boat and looking for gators.

There are many lakes and bays and bayous just a few miles south of Lafayette and probably more of them south of Baton Rouge. If you want a really nice Sunday drive, pack a picnic lunch and dinner, then you might try taking highway 82 from Palm Island State Park toward White lake and maybe all the way to the Cameron ferry. If you want a really long cruise you can continue on to the Sabine Pass Lighthouse to Sabine Lake on the Texas border. I don't know the ferry schedule so you would want to check ahead.

The Atchafalaya River flows south between Lafayette and Baton Rouge. If you like river boating there's your huckleberry.

If by chance you are passing all the way east through New Orleans, you can try their famous chicory coffee at the Cafe du Monde right down town. I've actually never stopped at their cafe, but I really like their coffee and I'm going to resupply soon, and if I ever get the time and chance I would visit their cafe to get it before it is canned.

Acadian Village has reconstructed old-style homes along a bayou. There are some museums in the area. I would check with the local colleges and universities. For example I visited a museum at Penn State that had gemstones like emeralds and rubies and diamonds almost the size of golf balls. You never know what wonders some universities have hidden in their art and natural history museums until you see them.

No visit is complete without checking out some hole-in-the-wall thrift stores. Just say'n.

If you have never eaten gumbo or jambalaya now is your chance to find them.

Also you might find spring rolls made with crawfish.