It is roughly 20 km from Sheremetyevo International Airport to the Mitino Hotel. As all public transport options require you to travel into central Moscow and then back out north to the hotel, taxi or transfer is definitely the best way to travel.
By taxi
If you take an official taxi from Sheremetyevo to the Mitino Hotel, the journey will take about 20-30, and will cost approximately $40 for the trip. Alternatively, you can pre-book a transfer with a driver to meet your flight here.