Anything besides Thai food is a little difficult to find in Phetchaburi. Western cuisine should ideally be avoided while here. If you want to be safe, you can eat at the hotel restaurants. Many local roadside small restaurants also serve incredibly delicious Thai and Chinese food. Khanom Thai is a candy like dessert that Phetchaburi is known for. Most street-side stalls here are open till late night too.
Mainly famous for its Thai food and being a town where it is next to impossible to find vegetarian food, options here are almost nil. Some vegetarian and vegan friendly restaurants are Anutra Je and a few street stalls sell some variety.