Bangkok is the capital city of Thailand that offers several things to do. If you happen to be in Bangkok during the weekend, you are lucky. Some places such as markets in Bangkok are open only on the weekend. Usually, many visitors spend about 3-4 days in this city. However, if you have only 2 days and they are weekends, here is the recommended itinerary.
Day 1: Visit the old town and the biggest outdoor market in town
I recommend you to start your day early and visit the 3 must-see temples which are close to each other. The first one is Wat Phra Kaew or Temple of the Emerald Buddha (and also The Grand Palace). The second one is Wat Pho or Temple of the Reclining Buddha. And the third one is Wat Arun or Temple of Dawn. The last one is located on the opposite side of the Chaopraya River Bank.
Visiting all 3 temples should take you more or less 4 hours. You might find something to eat around there and have a rest. Then, in the late afternoon, take BTS Skytrain to Chatuchak Weekend Market or is known as JJ Market. It is the biggest outdoor market in Bangkok and also in Thailand. Since it is huge, I recommend you to do some research before going there. Below is links related to this market.
Day 2: Visit a floating market and shopping places
On the second day, I recommend you to visit a floating market. Actually, there are several floating markets in and around Bangkok. If you do not have much time, I recommend you to go to the one that is located in Bangkok and not far from the city center (Siam Square) is Taling Chan Floating Market. However, if you plan to start the day early, you might go to Damnoen Saduak Floating Market. This one is the most famous floating market in Thailand and it takes about 2-hour drive from Bangkok.
After visiting a floating market, I recommend you to do some shopping in Bangkok. As you may know, this city is a shopping paradise, where tourists can purchase what they want at competitive prices. Siam Square, a popular shopping and entertainment area, and the surrounding might be a great choice. There are several malls in this area such as MBK Center, Siam Square One, Siam Discovery, Siam Center, Siam Paragon, and so on.
If you choose Taling Chan Floating Market, you will have more time for shopping. But if you choose Damnoen Saduak Floating Market, you will have less time for shopping. It is your choice.