Furnished Apartments For Rent In Galveston Tx . A 2 bedroom apartments averages $1,360 and ranges from $496 to $2,312. Based on our current inventory, the average size of a studio fully furnished apartment rental in galveston, tx is 216 sq. 7000 Seawall Blvd 513, Galveston, TX 77551 1 Bed, 1 Bath Townhouse from www.trulia.com See all 284 apartments in galveston, tx currently available for rent. 1 to 2 bedroom $1,050 to $1,250. An apartment home in this town costs from $400 to $2,622.