We just moved here too and are looking for good places to take the kids. According to another post, there is supposed to be a seminar this Saturday for things to do with kids in Bangkok. My wife found a small indoor park at the Emporium Mall, 4th floor. I googled the Discover and found this:
Open: 9:00 - 17:00 (Tuesday to Friday), 10:00 - 18:00 (Saturday to Sunday) Location: Chatuchak Park MRT: Chatuchak Admission: Adults 70 baht, children 50 baht Contact: +66 (0)2 272 4575