Nan is an area that hasn't been spoiled by mass tourism, so it's an ideal place for people who like to go off the beaten path. Nan is a typical provincial town, with empty streets and a slower sense of time.
There is a significant cultural legacy with the primarily northern style temples, especially Lanna. It's easy to combine a stay in northern Thailand with Chiang Rai and Phayao.
You can tour the city on foot, because everything there is to see is concentrated in the city center. There are the Nan National Museum and the textile museum, which are worth a little visit. As for temples, I recommend Wat Phumin, which was just renovated. It's beautifully decorated and has unique murals. Right out in front, I was able to attend a course between a monk and his apprentices at the temple of Wat Phra That Chang Kham. A short distance away, the 600-year old temple of Phrathat Chae Haeng is also worth a little side trip.
For a nice evening, I like the atmosphere of the night market not too far from the river.