Benjamin, first of all, once you will go to Eastern Europe or Asia, please be sure, that your mobile phone working with 900/1800Mhz frequency, instead of 850/1900Mhz frequency, as it used in USA.
From my side, I think, that good phone for your trail will be Nokia N82 - it have built in GPS, 5mpx camera,Xenon Flash,Wi-Fi, acceptable standby time as well as other smartphone functionality like radio, MP3 player, SD card support etc.
All Eastern European countries use GSM as well as Mongolia/China have GSM operators also. Belarus and Ukraine have 99% coverage as well as Russia/China and Mongolia have worse coverage.
Also, to save your $$ you may consider to buy so-called "Travel-SIM" card. It will allow you to roam over this countries with single phone number as well as having free incoming calls in more then 30 countries as well as cheap international calls. In Ukraine you may get SIM-card virtually everywhere. In Belarus and Russia you will be required to present your passport in order to buy SIM-card.
Hope this will help a bit.