Hi, I spent 6months over in St Petersburg and also some time in Moscow. St. Petersburg is the better city, it's older and has more character. The winter palace is a must to visit, and all the cathedrals are stunning, so id recommend to see as many as possible. Shame you'll miss the white nights, they are between June and July.
What to avoid, the underground is deep, really deep! Try to avoid it at rush hour if possible, it gets very busy and hot.
Other than that, enjoy- you'll have a great time.