Banks and licensed moneychanger booths (marked obmen balyot) exchange US dollars provided the notes are post 2003 and unblemished, in near-mint condition. Trying to get change for a 5000som note will likely be met with a look of horror.
There is no black market for currency transactions and changing money back again is not problematic. We quote prices in the currency that the businesses themselves use. That's normally som, but can be US dollars or euros for some hotels and tour companies.
If you need to wire money, MoneyGram has services at main post offices and Western Union works through many banks.
Travellers cheques are hard to cash but ATMs are increasingly common in all major towns. Most dispense both US dollars and som and work with Visa, but the whole country has under 20 ATMs that accept MasterCard or Maestro, mostly Kazkommertzbank. These are most usefully in Bishkek (10 locations), Osh (3) and Cholpan-Ata (1).