Is it safe to take a two year old child to Bangkok?
Has anyone done this?
Is it safe for them to eat the Thai food without getting stomach bugs?

When are you going to Bangkok? What price level hotel will you be using in Thailand? Are you going to be sleeping in dorms with total strangers sleeping near your child? Using dorms with total strangers sharing toilets and showers with your child? Or will you have your own private room, with your own toilet and privacy?

What kind of food do you want to feed your kid - street food with an unknown age and low sanitary level? Many backpackers eat cheap street food but they are old enough to make their own decisions and if sick they can handle it. I have been in and out of Asia for over 25 years and there are very few things I eat off the street. But there are those tourists that frequently eat street food without problems. I wouldn't experiment with a 2 year old Farang kid.

Have any tourists taken young children with them - yes they have! Thailand has excellent supermarkets. You will find milk, cereal, sandwich fixings. Instant soup, orange juice, and some canned food. BEFORE you leave home break your kid in on fried rice and maybe some other Asian style foods. Fried rice is cheap. If your kid is a runner maybe consider a harness! You keep a dog on a leash so he doesn't wander out in traffic why wouldn't a kid be more important?

You have a lot of McDonalds, KFC, Burger King and other chain restaurants you will recognize too. You must buy drinking water and not drink the water coming out of faucets. With the kid use the bottled water for teeth brushing. Tourists do not drink water from faucets, besides some of the waterlines in Bangkok may be compromised because they are in flooded areas and worse than normal.

Google up this question and see some other comments. When will you be arriving in Bangkok? Right now they are experiencing a flooding problem in part of the city. Hotels nearer the river are more prone to flooding. There will be debris to clean up. But other areas of Bangkok, areas close to the Skytrain, are not flooded. Some tourists right now are staying in hotels in Sukhumvit, Siam and other areas of the city. If you are intending to visit Thailand right away keep up to date with flooding progress. Because of the flooding in Bangkok some of the stores have had a run on water and bread. But there are many stores to choose from.

For Bangkok I would choose a hotel near the Skytrain route. The Airport Rail Service and Skytrain are elevated rail services. They connect many places in Bangkok. Some hotels, like the Khao San Road area, do not have access to the Skytrain.
UrbanRail.Net > Asia > Thailand > Bangkok Metro

Visit a library and check out a few travel guides. Some of those travel guides will have some information on traveling with children. There are other areas in Thailand to visit than just Bangkok. Work up a budget and see how much you want to spend on hotels and everything else. If you need hotel advice mention your price range.

Good luck.