Driving habits of some Russian drivers may seem crazy only if you have never visited New York City. Otherwise, you will agree that drivers in NYC are way crazier.
We would like to discourage you from stopping any cabs on the street. There are plenty of licensed taxi companies here.There is a choice of numbers you can call for a taxi 24/7, a car would usually arrive within 10-15 minutes of your call. It is quite cheap - taking you across half a city would set you back 5-10 US dollars.
Your Russian may be rudimentary and they will text you the make, model and license plate of the coming car.