My cozy house in central Baku is ready to accommodate you.
The unit is very big with 3 rooms and a big hall. There are 2 toilets, WiFi, 2 AC and lot more for comfortable stay.
Market works 24/7 inside the complex and many restaurants around are open until midnight. Also, Heidar Aliyev Centre (great sightseeing by ZHadid) is in 15 min walk away.
PS. Breakfast is included in the price and there are many amenities for cooking.
PPS. Picking up from the airpor can be arranged if you're interested