As an avowed non sporting person the whole soccer world cup mania is not my idea of a good time, but the chance to see even a little of Russia is definitely on my to do list.
I have just had clients spend four nights in St Petersburg and they made the most of their time there by booking a personal tour of The Hermitage, the world famous museum where they boast that if you spent one minute in front of every item in the museum it would take you eleven years to see it all. With over three million things to see your head will spin. Fortunately only a fraction of the collection is on show. While there the guided tour of the Treasury is worth a look for the gold room among other things.
St Petersburg offers majestic churches, the Nevsky Prospect to walk along, and trips to Peterhof. Try to avoid the ship loads of cruise passengers all trying to squeeze into the city of you can.
You can cruise on the river between St Petersburg and Moscow and take in the Golden Ring that takes you to ancient towns and wooden churches and a very different Russia from the two big cities. The train will also get you between the cities efficiently.
If trains are your thing, the Trans Siberian railway is a once in a lifetime experience. This will allow you to see the sheer scale of this vast country, meet the locals who depend on the train for communication, supplies and contact, and allow you a glimpse into a very different way of life.