We are going on the Grand Princess out of Galveston Dec 2. What do you recommend as far as driving to Galveston from San Antonio on the same day of the cruise and paying $7-$10 a day for parking? Or should we leave San Antonio the day before the cruise is scheduled to depart and stay overnight at a hotel to avoid rushing/traffic, etc?

I would drive in the day before then you are relaxed and ready for the cruise.
If you are delayed in traffic (not much between S.A. and Houston) but in Houston you could run into delays.
Check if there are any hotels that offer free parking for the duration of the cruise.
http://www.parksleepfly.com/cruiseport_hotels/index.php