Best dining experience in Moscow, hands down, is Cafe Pushkin. Even Time Magazine concurs.
It's a taste of old world Moscow service and ambiance where you'll be surrounded by pretty young things.
Go, eat dinner - I'd recommend the blinchiki with caviar.
But definitely save room to split a few of their desserts. Especially the flammable ones! These are easily the best sweet eats in the entire city.
We thoroughly enjoyed an amazing strawberry and pistachio Pavlova, and some delicious creme brule-sugar crystal domed-caramel sauce coated concoction that was heaven set aflame on a plate.