Wizz Air if offering a 20% discount for all flights and all destinations for Wizz Discount Members.
Travel dates: 11.12.2016-31.12.2017
I can be that on Monday this will be available for everybody!
I searched for an exotic winter vacation and I found Milan-Kutaisi for €67 (11-15/01). If you want cheper, try the next week for €39 (18-22/01).
For accommodation I recommend you to search on HotelsCombined as it aggregates all booking portals including Booking. You can find hotel reviews on Tripadvisor which is also great for searching best places to visit.
Hostelworld offers perfect budget accommodation for students, backpackers and low cost travelers.
If you want to stay with a local, you should rent a room, apartment or house on Airbnb. When you travel on Airbnb, you will get €18 in travel credit as my referral.
I suggest to rent a car from RentalCars if you want to drive around.