Accommodation at/near Tbilisi Airport

I've read a lot of previous posts by people arriving at Tbilisi Airport in the middle of the night, asking about transport into the city centre at this time, and a couple asking about the possibility of sleeping in the airport itself. However, rather than either of these options I'd prefer to stay in a hotel of some description in the immediate vicinity of the airport. My flight is scheduled to arrive in Tbilisi at 01.50, and as it's the first night of my trip I'd like to get as good a night's sleep as possible, before actually heading into Tbilisi properly the next day. Does anyone know of any hotels or hostels at, or very near to, the airport?