Hire a guide to tour the Kremlin, they are abundant around the front gates, so negotiate a price. The guides are licensed and wear badges. They speak English fluently.
The Hermatage in St. Petersburg, again, hire a guide for a full day if possible, or multiple days (it is worth it).
Visit any of the Churches. St. Basils on Red Square and The Cathedral of the Resurrection in St. Petersburg are a must see. Many are undergoing restoration. Shopping is best at the airport Duty Free, but you've got to visit G.U.M. in Moscow. and the grand shopping Avenues (getting more Westernized every day)
Quick Tips:
If planning a trip to Russia, get a language dictionary and study the Cyrillic alphabet (and pronunciation).
Since you must obtain a visa and an 'invitation' to visit, use the services of an experienced travel agent - Red Star Travel in Seattle is recommended.
Best Way To Get Around:
The Metro is extremely clean and efficient and cheap! An excellent way to move about (study your Cyrillic - there are no English maps except the ones in Guide books). Some of the Metro stations are beautiful, all are efficient and clean. If travelling between Moscow and St. Petersburg, do not fly. Take the overnight train (1st Class with a locking compartment)it may be the best nights sleep you have ever had.