Offering a Kremlin tour and Moscow City bus tour,  this is a good bet if you are looking to maximise your time. The Kremlin tour takes in the grounds, cathedrals and the Patriarchs Palace and will provide you with all the facts you'll ever want to know about the Russian tsars. The bus tour takes in a wider part of Moscow and technically you can hop and off it, although the buses don't go that often so i'ts best just to stay on the bus and suffice yourself with the 20 minute photo-taking/souvenir-buying break on the top of the Sparrow hills. The guides are very knowledgeable and have enough facts in the back of their heads to get you through even the worst Moscow traffic jam. All tours are conducted in English and include entrance fees. Booking in advance is recommended  (there's even online reservation) or you can just turn up to their office on the day.

Point of departure: Capital Tour's office. Kremlin walking tour costs 1550Rbl, children 775Rbl, leaving at 14:00, except Thu. Taganka Secret Bunker tour 1400Rbl, 1100Rbl children, leaving on Thu only at 14:00. Moscow All Around bus tour 1000Rbl, children 500Rbl, leaving daily at 10:30, 13:30, 15:30 from Bolshoy Theater bus stop (next to Karl Marx monument).