Manti dumplings is a must! There's a shop just off the center of town, facing the "BU Palace," which makes delicious manti soup. Has some other reasonable dishes as well, and usually has beer and soft drinks.
Pamukkale is a nice Turkish-owned restaurant, which food that is expensive for locals but reasonably priced for foreigners $2-3. Most plates come with a meat of some sort, shredded carrots, rice, and french fries; you can also get soups, and sometimes, cucumber and tomato salads. You can regularly get coke products, but not alcohol.
There's a Mongol-owned restaurant that opened up facing Pamukkale but a couple of blocks down, which is a little more expensive $4 a meal or so but has nice food.
Several smaller shops will have meat patties or manti for cheap, usually served only with milky tea.
If you're lucky, you'll find a shop or friends that serve delicious beshparmak Kazakh traditional food - lamb and noodles or horse sausage fat mixed with dark lean meat - very tasty!
You'll probably find it difficult to eat well as a vegetarian, and will only rarely find fresh fruit and vegetables.