Petchburi isn't really a tourist town. It does get a large number of visitors, but most of them are just stopping on their way to or from the beaches further south. As a result, it doesn't have much in the way of nice restaurants or cafes. Of course, there are places to eat, and even a few local coffee shops, but nothing fancy or worth noting.
Some of the Petchburi's famous sweets
Something that is worth noting is that the city is famous for its sweets. It is the center of palm sugar production in Thailand, and you can find a wide variety of things made from it. There are a large number of stalls selling the local products along the main road north of Khao Wang, as well as some stalls in the city's main market. Of special note is Ban Khanom Nuntawan, a large modern shop right on the highway that resembles a supermarket filled with sweets. They are well stocked with the local favorites, as well as the specialties from other parts of Thailand.