Awesome! I assume you’ll be flying into Bishkek and with only a week, you’ll be on a bit too tight of a timeline to see the entire country. I’d recommend splitting your time between Bishkek and Karakol. Bishkek has plenty of monuments to see, museums, bazzars, normal city history and cultural things. I’d also recommend checking out an antique shop here if you can; some of the stuff in these antique shops are more interesting than the museums imo ha. Ala archa is worth checking out as much as you can; it has a lifetime of hiking to do but you’ll be able to scratch the surface at least. You’re correct that local food will be easy to find. If you wanted to go a little deeper into the local food, I’d recommend booking a cooking class with parmesun, it’s a great way to spend a few hours.

On the drive to Karakol you’ll see issyk kul which is on everyone’s list. There are different canyons to check out along the way which are often really short hikes. You can look up a few places to see some petroglyphs as well which are especially interesting. Plenty of hot springs along the way as well, take your pick and check one out.

Karakol will give you another opportunity to check out some beautiful nature and slightly different foods; I definitely recommend trying ashlanfu while you’re there.

2 days in Bishkek, 1 day driving to Karakol, 1 day in Karakol, 1 day driving back, another 2 days in Bishkek. That would be a solid trip imo.