Washing in hotels is quite expensive and in some of them not available at all. Don't forget to take special gifts for the people you are going to visit and some more small souvenirs. If you are visiting your lady, take pictures of you, your house, your city etc. Though during the last years traveling to Russia became easier, you still have to obtain a visa. You can apply for a private, tourist or business visa.
Tourist visas are the least complicated to obtain.
When you choose a travel agency, make sure that they have a reliable Russian partner in the city you are going to visit, otherwise you can be lodged in a low class hotel somewhere in outskirts. It's important to be met at the airport by an English speaking person and you'd better arrange it from home. You must register with Russian authorities after arrival to the destination. If you are staying in hotel, the administration will do it for you. You should have a contact in a Russian tourist agency in the city to solve problems if they appear.