Finding reasonable airfare to Moscow during summer months is usually a tangled feat at best. But Finnair is showing fares on Orbitz today for $520.68 after taxes and surcharges. Dates for this specific rate are Sunday August 16th with a departure from JFK at 5:40pm. Your return flight leaves from Moscow on Monday, August 24th at 12:50pm.
You could spend more than your airfare costs at The Savoy Hotel for approximately $570 a night and live it up in luxury. Or you can spend about $190 in August and step back in time at the Ukraina Hotel. It's not a typical Westernized hotel with all the frills and amenities. It's currently undergoing a revitalization to offer more luxury standards, so rates may spike, especially during summer months.
The Zvezdnaya Hotel is also another option for a reasonably priced hotel. Don't expect the Ritz, but you will get a comfortable and clean room for roughly $90 for a single standard room a night. For cheaper rates, look to outer suburbs in proximity to local transportation to cut costs.
The Maximia Irbis Hotel (about 10km from the city center) runs about $100 a night in August. They are showing a possible "hot water shortage" for the month of May due to municipal works, but hopefully by August everything will be warmed up again. Trip Advisor ratings do show complaints that it's a hotel for "Cold water enthusiasts" and others are disgruntled with taking the metro to the city. But overall, it's a decent place for a relatively inexpensive option in one of the most expensive cities in the world.
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