It is very difficult to get a Russian visa without a hotel booking. However specialist tour operators to Russia can make individual arrangements at a wide range of hotels, which secures a visa automatically. It would be a pity though to limit travel just to Moscow and St Petersburg. Take the opportunity of staying in towns along the Golden Ring such as Suzdal and Yaroslavl. For mid-range hotels in Moscow, allow about 50 a night for a twin, and in St Petersburg about 60.
Prices are lower elsewhere.
At Easter an airfare into Moscow and out of St Petersburg should be around 300. I suggest you contact Intourist and ask for information as an independent traveller. The company can book hotels, flights, travel within Russia and arrange visas all at a reasonable price. The Pulkovskaya is also good value, but some distance from the centre. The Astoria has particular grandeur, style and location but is more expensive.