New Orleans:
- The Voodoo Museum in the Quarter
- Oak Alley Plantation, or Houma House Plantation.
- Friday lunch at Galatoire's. It's not just a meal, it is a quintessential old-school creole New Orleans experience. You have to get there early in the morning to put your name in, but it's worth it. If you can't take the time, then go for dinner. They take reservations for dinner (upstaire dining room only, which isn't quite as cool, if you want to sit downstairs have to take your chances) It's business casual for lunch, jacket required for dinner.
- Do a swamp tour, an airboat trip through the swamps, very cool, you get to see a lot of alligators and birds
- Audubon Aquarium
-WWII Museum
-Beignets and coffee at Cafe du Monde, any time of day, but especially for breakfast or late at night (open 24 hours)
- Drago's Oyster Bar
I think 5 nights in Memphis is a lot, I'd cut that down to 2. 3 tops. You could do it in one. Nashville has more than Memphis, but I'd keep that to 3, max. Loveless Cafe is a quintessential Southern diner with stick to your ribs southern dishes, especially for breakfast. The Hermitage is a good visit.
With the time you save cutting nights off your Memphis and Nashville stays, visit Chattanooga, it is a beautiful city, with a lot of great outdoor activities. Lookout Mountain is a nice spot.
Camp in Great Smokey Mountains National Park. You can rent cabins so you don't have to worry about camping gear. Otherwise stay in Gatlinburg.
We went to Savannah and Charleston for the first time three years ago. Before we went, everyone said "oh skip Savannah, just go to Charleston", but we're really glad we went to both.
Houston - I was born and grew up here, moved back after college, I love it, but I always say "it's a nice place to live, but I wouldn't want to visit." Is there anything particular you want to see here? We're not really a tourist town, don't have a lot of sites, and are generally a nondescript modern Sunbelt American city. If you want a real flavor of Texas, I'd recommend San Antonio instead. It is a really neat city. Take a bicycle tour of the Spanish Missions, it'll be the perfect weather for that in April. Don't just stick to the Riverwalk, visit the Prince William District and have brunch at historic Guenther House. Lots more to do in San Antonio that I can't think of right now.
If you're dead set on Houston, at least the weather will be really nice when you're here. If you're at all interested in space exploration, Johnson Space Center is worth a visit. Galveston, an island an hour drive south of Houston, is nice. The beaches aren't anything to write home about, but the historic Victorian downtown is extremely well preserved and lots of shops, restaurants. The Elissa, a tall ship from 1877 is worth a tour, as is the Texas Seaport Museum, and the Oil Rig Museum, an old decommissioned oil rig that's been turned into a museum so you can see what life is like on one. They're all right next to each other. Gaido's is the institution restaurant on the island since 1911. Back in Houston, we have several very good art museums, especially the Menil. We have too much good food and varied cuisines for me to even begin to list some, we've emerged as one of the top 5 food cities in the US in the last few years. Ok, I'll try to list a few standouts - Pass&Provisions, UB Preserve (formerly Underbelly), Reef (unique Gulf Coast seafood restaurant). Also, we have a very large Vietnamese population, with excellent Vietnamese food all over the city, but especially along Bellaire Boulevard just inside and outside Beltway 8 (Sam Houston Tollway)