Like all Thai cities, Phetchaburi has hundreds of restaurants and cafes, serving almost every variety of Thai food. Many of them specialise in just a few menu items, so the trick is to decide what you want to eat before you decide on where to eat. There is almost no English language signage, so specific recommendations are not especially helpful. On the other hand, whichever of these cafes or restaurants you choose to frequent, your chances of not being served a wholesome Thai dish are very low.
If you wish to be "safe," the two hotels mentioned below have restaurants that will likely not disappoint you. In addition, the Big C has several Western-style franchises under its roof e.g., Chester's Grill, KFC, with air conditioning and English language menus. But be advised this establishment suffers from severe noise pollution.
Apart from a few Chinese restaurants, the aforementioned Big C franchises, and two pizza parlors in peripheral locations, anything other than Thai food is almost impossible to find in Phetchaburi city.