I need to stay for one night at Sheremetyevo International Airport in Russia and I am looking for a cheap airport hotel (30/40 $ per night), preferrably one that is located within the airport. However, as far as I know, I could not find such hotels. Do I need to find a hotel outside the airport?
I found Midland Sheremetyevo Hotel to be the cheapest, but if anyone who knows better places or suggestions, please let me know.
Only myself (single adult male) will be staying at a hotel.
I'm fairly sure the price range you're asking for is impossible.
For close to a decade, Moscow has been the world's most expensive city for business travel, with hotel rooms costing a ludicrous $414 per night on average according to the linked survey in 2013. Even the "V-Express" capsule hotel in SVO, reputedly the temporary home of Edward Snowden, wants 2450 RUR (~US$75) for a mere four hours in a glorified coffin.
There are hostels in central Moscow that can get you a dorm bed for 600 RUR (~US$20), eg. Napoleon, but you'll be sharing the room with half a dozen strangers. None that I know of are particularly convenient to the airport, and the train ride costs 300 roubles one-way, so you're already up to $40 even for this. You could theoretically shave off a few kopecks with buses or local trains, but none are convenient or recommended for a first-time visitor.
