December is not a usual time to go to Russia as a tourist, and Russia is not a usual destination with a 2 year old. So, if you can give us more details of why you're going to Moscow and St. Petersburg in the first place, we can give better advice.
What the visa situation is will depend on your nationality. If you are a US passport holder, it's not easy or cheap to get a Russian visa, but it's certainly doable. For other nationalities, it can be much easier (one poster here explained that as an Israeli passport holder, she could enter without needing a separate visa at all). If you do have to get a visa, be prepared to use an agency to help you, as it's just not easy on your own. And do be sure to follow their rules to the letter, or your visa application will be rejected.
I agree with lachera - if you're going on your own, you MUST learn the Cyrillic alphabet. It's not hard; I used a book called Teach Yourself The Cyrillic Alphabet, which appears to be out of print. However, a similar book is here on Amazon: http://www.amazon.com/Teach-Yourself-Beginners-Russian-Script/dp/0071419861/ref=pd_sim_14_5?ie=UTF8&refRID=0YQYF6CS236PH2H02NBV&dpID=41OoOBFovwL&dpSrc=sims&preST=_AC_UL160_SR98%2C160_
This book breaks the alphabet down into letters that are the same as English, those that look the same but have different sounds, those that make sounds we don't have in English, etc. As lachera said, there is almost no signage in the Roman alphabet, so you really must be able to decipher Cyrillic and sound it out (even if you don't know other aspects of the language).
As for best sights, a guidebook will answer that question better than a forum can. For St. Petersburg, all I can say is don't miss the Russia Museum. The Hermitage is more famous, and has great art - by artists you can see in other museums. But the Russia Museum has stuff by local artists you can't see elsewhere, and it's wonderful. Don't miss The Wave by Aivasovsky - breathtaking. The Church On The Spilt Blood is also amazing. And I loved both the Yusupov Palace and the Sheremyetov Palace (the latter is now a museum of musical instruments).
In Moscow, Red Square, The Kremlin, Lenin's Tomb, etc are the famous sights. Do make sure to see the fancy Metro stations, like Mayakovskaya on line 2 and almost any station on line 5 (the ring line). And a great lesser-known sight is the Gorky House, an Art Nouveau wonder.
Budget? Like any city, there's quite a range, and your cost will depend on your needs and wants. Accommodations in these places are expensive. In St. Petersburg, I stayed at a nice place in a great location with a shared bathroom for only €80 per night, but with a 2 year old you probably want a private ensuite bathroom. For food, do you want to eat in restaurants for every meal, or can you get stuff from a supermarket? Some sights are expensive, like the Hermitage or the Kremlin; others are much cheaper. A ten-trip ticket on the Moscow Metro is a bargain; a taxi or private car is not. Etc.