Duet Hostel and Cafe is the ultimate traveller hangout spot in Karakol. While I didn't stay there myself, I heard good things from others who did. But I did visit the cafe often.
The cosy café offers free Wi-Fi and a lounge where you can kick back and relax or get some work done. It’s a good place to meet people if you’re a solo traveller, and they offer free tourist information too.
They have a handy map of the Ala Kul trek that you can use to plan your trip, and the staff can provide information on transport.
Duet also has a whiteboard for travellers and hikers to find a buddy for treks. I know people who found other people to join with this system, so it’s perfect if you’re a solo traveller and prefer not to hike solo.
The food is pretty decent too, with coffee, local dishes and plenty of western options too, including burgers.