Bolivar peninsula is located east of Galveston Island is is accessible from the island via car ferry. The D.O.T operates the ferry and the fee is free. You can either take your car on or walk on for the 18 minute commute to the peninsula.
The beaches are less busy than on the mainland, just drive a few miles a take a random right. The road will end as you drive onto the beach.
Its a nice break from the city.
http://www.crystalbeach.com/chamber.html
