Kyrgyzstan is incredible. I’d recommend hiking to Song-Kul. Head to Kochkor and arrange a trip via the local CBT (community based travel). My girlfriend and I got a night in a home stay, taxi to and from the start/end points, two nights in yurts including all food and a guide for three days for about £90. You’re putting money into the hands of the community rather than your companies as well.
We headed to Karakol after that then hiked up to Altyn Arshan (not sure of spelling) where there are natural hot springs. From there you can head further up to Ala-kul lake as well.
Cholpon Ata Is about the only place that is geared for tourists around Issy-kul. It’s ok, full of Russians and and very commercial compared to the rest of the country. A few days is so you’ll need there really.
Bishkek isn’t much to talk about really. It’s very much am old Communist city with some nascent signs of becoming a bit for Western. Watch out for pickpockets in the market. Otherwise it was pretty friendly.
I can recommend some hostels etc if you like.