Old Customs House
Right at the banks of the Chao Phraya River, the Old Customs House is right where the 19th-century port of Bangkok used to be. Now it is a crumbling building which needs a lot of renovation to get back into a useful state, but its obvious that this grand colonial-style home was once the pride of the area. It was built in the 1880s and used to levy taxes on traders that moved in and out of Siam. It's not open to the public, but you can walk around and try to grasp the atmosphere of Bangkok in the 19th century. It was used in Wong Kar Wai's In the Mood for Love, a Chinese movie that's worth the watch.
Neilson-Hayes Library
Visiting a library during your trip might seem a bit odd, but this one might convince you. The library has the largest collection of English language books in Bangkok, catering to the many Western expats in the area. There is also an art gallery, a café, creative workshops and plenty of events throughout the year. Also, the European-style building from the late 19th century is of great architectural interest.