La Porte isn't bad. It's an old town surrounded by the port and all that goes with it
Depending on how long your cruise is it might be best to just rent a car. IAH is about 35-40 minutes away. Cabs in Houston are rather high. A town car should be about $50-75 if you want to go that route. I'd recommend Action Limo at 713.781.5466.
Since it looks like you're not spending a lot of time in Houston itself you might just want to spend the night in La Porte. The nicest place will be the Comfort Suites at 902 S. 8th Street, La Porte 77571 - 877.424.6423. They might even have a shuttle to the port. It will only be about 3 miles away. If you stay in La Porte have dinner at El Toro at 616 W. Main (walking distance from the hotel).
If you want to stay close but in a little more fun area try the Hilton NASA Clear Lake at 3000 NASA Rd. 1, Houston 77058 - 281.333.9300. It's directly across from Johnson Space Center and on Clear Lake. Will have good views of the lake and marinas or NASA from the rooms. Will be about 15-20 minutes from the port via NASA Rd. 1 and HWY 146. Plenty of cool night life on the waterfront as well as restaurants. For something nice try Perry's Italian Grille at 1001 Pineloch, Houston 77062 - 281.488.2626 (make a reservation). You'll want a rental car if you go this route for sure.
About the same distance away as the Hilton you can stay at the Kemah Boardwalk on HWY 146. There is a small hotel, tons of restaurants, bars, shops and carnies. One of the best tourist attractions in Houston. If you go here have dinner at The Flying Dutchman (reservation shouldn't be necessary). Visit the website here Kemah Boardwalk
Give me a call if you want to grab a beer while you're here. I'll buy the first round