For me this was more about visiting the province between Bangkok and Nan. The Nan River actually flows through Phitsanulok, and there is a night market close by it. The problem is that as you visit Thailand's towns and cities you become bored with temples, yet there isn't much else to see except temples in Phitsanulok. I restricted myself to Wat Phra Si Rattana Mahathat(also known as Wat Yai), which is the most famous of them.
After that I perhaps didn't really make enough of my time there to really appreciate the city, being aware as I was that it's a destination regularly visited by travelers heading for Northern Thailand. There is of course a national museum and a folklore museum there, which are two other things of interest the city has to offer. To sum up, I don't consider Phitsanulok a must-see destination when visiting Thailand.
I stopped at Phitsanulok when I went to visit the temples of Sukhothai and I remember a fairly large town, with wide streets where tuk-tuks were replaced by rickshaws!
What I remember most about my visit to Phitsanulok is Wat Phra Si Rattana Mahathat, a beautiful temple where there is a statue of Buddha, one of the most sacred in the country, which draws big crowds to gather in front of it. And speaking of statues of Buddha, why not do like I did and visit the factory which makes them, so you can see how they are hand made and decorated. An interesting and original trip.
Apparently there are some beautiful national parks in the area, especially Thun Salaeng Luang, but I didn't have the time to explore them as I was continuing my journey around Thailand.