Bangkok is a wonderful city and has variety of accommodation from budget to luxury. If you need a place away from night clubs and casinos then try to stay a little out of town along the river. I suggest you the Royal river hotel which is located in a quiet area and a perfect place for a family. Actually Bangkok offers wide range of accommodation near the airport, in the downtown, riverside, Silom area and in Sukhumvit, so choose the best one among them and have a comfortable stay:)
Since you are going with a child to
Thailand, better rent a car and visit all the places. Bangkok has many things to see including the wonderful palm fringed beach, Dusit zoo, the Crocodile farm and the Rose garden.
Emerald Buddha Temple and the Temple of the Dawn are some of the must see places, so don't miss them. I just reached
Phuket from Bangkok with in an hour and it's also a fabulous place to visit. It's having the finest
beaches of Thailand, I nearly spent a week here and had more fun. Hope you have too!