My suggestion would be to rent a car from Enterprise. They have a drop off across the street from the cruise terminal. If you come in a day early you would also have transportation to get around Galveston.
You can pick up an Enterprise car at either airport.
If you are a group, check with Supershuttle. They don't normally run to Galveston (last time I was there), but you can rent an exclusive shuttle and go where you want.
From Hobby (was more from IAH), I think the cost was $100 (plus tip) from Hobby for a bunch of people.
The road to Galveston can become gridlocked at times - especially if they are doing construction. If you are going to try to fly in the day of the cruise - I never advise that - plan on it taking longer than it should to get to Galveston. If it doesn't, you get to start eating that much sooner.
I've rented from Enterprise for several cruises from Galveston. The total for the rental has run from about $50 for a full size car to about $80 for a minivan or SUV.
That would include the dropoff fee. As I said you would then have the use of the vegicle while in Galveston and a ride to the pier. They usually don't have a dropoff fee when returning the vehicle from Galveston to the Houston airports either, so the price was $25-$40 cheaper going back to the airport.
That sounds about right. I use to pay about $25 for a full size Enterprise. There may not be a drop off fee on the return, but I thought the daily rental rate was higher.
Last November, it was an easy walk from my hotel to a liquor store and Kroger was across the street. We also had a number of restaurants to choose from for dinner. I really had no need for a car and didn't have to deal with dropping it off the next day.