By taxi
It will take at least 90 minutes to reach the Art Hotel by road from Domodedovo. Official airport taxis currently cost roughly $75 (for an economy-class sedan) or $85 (for executive class sedans and MPVs). If you prefer, you can arrange a transfer with a driver to meet you at the airport here.
By train
The Aeroexpress rail link runs from Domodedovo to Pavelets Station in central Moscow. The service operates daily every 30 minutes from 6am to 12am. The journey takes 40-50 minutes and standard adult single tickets cost around $11. From Paveletskaya Metro Station, it is a direct journey eight stops north to Sokol, which is around 15 minutes walk from the Art Hotel.
By bus
There are buses running from Domodedovo to Domodedovskaya Metro Station in the far south-east of Moscow, but considering that the combined journey and walk to the hotel will take nearly two hours, this is not really a viable option.