What is the wettest part of Russia?

Answer 1

On the website of the Russian Hydrometeocentre there is a map showing the Average Monthly Rate of Precipitation on the territory of Russia:
http://meteoinfo.ru/climate

Generally, the amount of precipitation decreases as you go from the North West to the South East of Russia. The exceptionally wet region in the European part of Russia is KALININGRAD OBLAST, with over 700 mm of rainfall a year. (For comparison, the stats for Moscow are 553 mm/year.)

The FAR EAST of Russia experiences 600-900 mm/year, thanks to the summer monsoons (compare that to the Eastern Siberia which gets less than 400 mm/year). So, to answer you question, the Far East is the wettest (and the snowiest!) part of Russia. Particularly wet is the KAMCHATKA PENINSULA: 1000-1200 mm/year (although again, not all of it is rain of course).

The amount of precipitation changes with altitude as well. In the CAUCASUS MOUNTAINS you get around 1400 mm/year.

The website I mentioned above shows graphs with average temperature and precipitation for all major Russian cities:
http://meteoinfo.ru/klimat_gorod

For example, here are the stats for Moscow:
http://meteoinfo.ru/MoskvaClimat
The top graph shows average day (pink line) and night (blue line) temperatures over the 12 months.
The second graph shows the average amount of precipitation (dark blue line) and the average number of rainy days every month (light blue line).

That website is in Russian, and if you need information about any other particular city, let me know!

Answer 2

The lakes and rivers.

Sorry - couldn't resist that one.

The northern and eastern edges.