Go to Kolоmenskoe. You can walk in there for miles. Be sure to visit the wooden palace there. Easily a half a day experience.
Go inside St Basil's on Red Square. And Christ Savior cathedral where the famous Pussy Riot event occurred.
And there are a couple of art museums right near Christ Savior.
Actually, all kinds of churches. The ones in Moscow are older than the ones in Petersburg, which was founded in 1700.
Take a bus out to Сеергиев посад, the seat of Russian Orthodoxy. busses leave from ВДНХ.
Аh, Petersburg! take a hydrofoil out to Петергоф, spend the afternoon wandering around the gardens.
the Hermitage, of course.
I didn't do this, but stay up and watch the bridges go up, somewhere around 2am. Make sure you're on the right side.

Have a great time, I know you will. I've been there several times, the longest, one month in Moscow. Need more time there.