Just inside the western gate to the city and next to Wat Chedi Luang is the Chiang Saen branch of the National Museum. The museum is a good starting point if you're planning to spend some time looking around. There are pictures of the major temples around town, as well as artifacts recovered from various excavations. Some of them date from pre-history.
There's a 30 baht (0.78 USD) for entry to the museum for westerners. The museum is open 8:30 am to 4:30 pm from Wednesday to Sunday.