Without knowing your interests and the no.of days you plan to spend in Thailand, I'll suggest two day trips - one day to visit the Summer Palace and ruins of Ayutthaya (former Siamese capital that was destroyed by the Burmese), and another day trip to Hua Hin, a popular weekend retreat for Bangkok residents.
If you are amenable to venture further afield (at least 3D/2N), you can either take a luxury train ride on the E&O Express or a short flight to Chiangmai in the north, where the weather is cooler and the lifestyle/pace more laid back than Bangkok. Here you can visit the stately Doi Suthep hilltop temple, watch Northern Thai cultural show with 'kantoke' dinner, shop for Thai handicrafts (much cheaper than Bangkok) or even visit an elephant sanctuary. Browse TA's things to do lists for Chiangmai and Chiangrai.
If you like tropical beach holidays, consider a side trip to the beach resorts in Southern Thaiand, such as Ko Samui (beautiful pristine beaches, laid back vibe) or to Phuket (popular but touristy and rather crowded). Better value, and safer, than a beach holiday to Bali in Indonesia and Boracay in Philippines.