Kyrgyzstan, and Central Asia in general, doesn't really have a great reputation for food. No one travels here for the food, and that's probably reasonable. But if you're coming for other reasons, the food can be one of the side benefits of coming here, especially if you know what you're looking for.
Kyrgyz food is good once in a while, but it's mostly meat, white flour, onions, and fat (beshbarmak and oromo are perfect examples). In the right hands it can be truly amazing (one of our best friends here is an excellent cook), but usually it's just okay. The exception to this are samsas which is nice because they're great street food. You can always find meat samsas, but if you look around Bishkek, you'll see potato, cabbage, jusay, cheese, mushroom, and other fillings. Different fillings are popular at different times. Just look around a little.
Some Central Asia foods like manty are pretty similar whether they're Uzbek or Kyrgyz or whatever, but most things are better if you don't get the Kyrgyz version. Uzbek plov is always better than Kyrgyz plov, for example, at least in my opinion.
Fried pelmeni is also a really tasty treat.
When it doubt, go to a minority cafe. Dungan and Uyghur cafes are all over Bishkek and you can still get your traditional Kyrgyz foods if you love them, but you also have other choices like laghman. Ashlyamfu is a really good Dungan dish, and so is ganfan, and anything make with sparzhe (tofu sticks) or funchyoza (bean thread noodles). There is also some amazing Korean food here.
I always like shorpa, the clear soup that is often served at the beginning of a meal. Meat is simmered in broth, then you add vegetables. They're usually not cut very small so you get a bowl of broth with a hunk of meat of some kind, a small potato, and maybe a carrot or a radish in the soup. It's usually garnished with dill.
Shashlik is good too, although it's also really dependent on the cook. It's hard to mess up shorpa, but it's easy to make nasty shashlik.
I love the salads. There are some Russian-style salads with too much mayonnaise, but mostly they don't have mayo and they're delicious. One of my favorite thing about going to a wedding is trying the salads. A Central Asian salad cookbook would be amazing.
And don't forget the bread. I like all types of tandyr naan, of course, but I also really like the Kyrgyz domed bread that's baked in an oven. It's also really easy to make at home. And I cannot think of the name right now. It's not very easy to find in Bishkek, but if you get out of the city, you're probably more like it find it than tandyr naan, at least in the north.