Kyrgyzstan has the easiest visa rules in Central Asia.
It should be no problem to get your 30-day Kyrgyz visa in Tashkent or Almaty.
You don’t need a letter of invitation and the cost is about $55 U.S. for 3-4 day processing or double for a same-day express services. If you are flying, visas are issued on arrival at the airport.
Once in Kyrgyzstan, your visa can be easily extended in Bishkek on the same day for 1,055 Som. The extension is done within a day and starts on the day you go for a renewal (not from the end of your visa). It’s also possible to renew your visa in Karakol.
Most nationalities do not need to register their Kyrgyz visas. If you do need to register, it’s a one-time registration. Hotels don’t generally ask to see your passport.
In addition to your visa, you will need a permit to cycle some of the remote parts near the Chinese border. Authorities in Karakol can issue the necessary papers.