Get the visa first for sure!
Although I don’t think you will have any problems if you book your flight in advance (in case you have 3-4 months left until the date of your trip).
As for places, what are your expectations and your budget? Staying at hotels in Moscow is pretty expensive nowaydays. The best idea is to explore the Russian hospitality and enjoy the cosiness of your friends’ houses :).
Drop me a line to dima(at)uralov.com, I’ll try to get you some new Russian friends :)