I cannot comment on hotel options but there are two airports in the Houston area (Galveston does not have any commerical air service). The main Houston airport is Bush International (IAH) and is a little over one hours drive to Galvestion. The second, smaller, airport is Houston Hobby (HOU) and it is about 30-40 minutes away from Galvestion. Both airports have direct service to many parts of the county, but IAH has the most options by far.
My husband and I should visited Galveston for a weekend. We were curious about the cruise port and what was available there. The Harbor House Hotel looks convienent to the port and is among several restaurants. I don't know about the price or amenities, but I bet the internet has alot to offer. There is also plenty of shopping in the area as the hotel and pier are located near the "Strand", which is set up with many small shops. Then, there is of course the Historical Estate Homes and the Gulf. I am not 100% certain about the transportation in the area, however I did see taxis, a trolley and horse drawn carraige. Regarding meals, as I mentioned there were several places in the immediate area. We ate at Joe's Crab Shack and it was delicious. I was surprised actually. I am not a big fan of chain restaurant foods as it usually is only glorified fast food, but the crab legs were out of this world. Yes, they were brought in from somewhere, however, the meal was prepared perfectly.