I live here in Bangkok.
There is a huge sports building across the street from Rahmkanheng University out Soi 71. Near the Hua Mark Stadium. It is called FBT. It is a seven story building with sports equipment on all floors. The tennis dept is outstanding. They will string up a new racquet for you while you wait (30-40 minutes). Pretty much any brand you can think of. They even have a small room with a wall where you can hit with a frame and see how it feels. I highly recommend you take a taxi out there and see for yourself if you have time.
Siam Pa-ra-gon is an expensive shopping mall, very new. The tennis dept there may fill your needs and it is much more convenient as it is right at the Siam BTS stop.