The most inexpensive flight times depart Istanbul late in the evenings and return from Tbilisi early in the mornings. Many nationalities require no visa or visa on arrival for both Georgia and Armenia.
Make sure that you inform the rental agency of your plans to cross the border at least a week in advance so the proper paperwork can be prepared. Once you are at the border, you will pay an additional $10-15 USD to the Armenian border officials to take your rental car across.
There are other options, such as hitchhiking (though language barriers will probably be an issue, or even individually arranging with a taxi driver to drive you down to Yerevan or vice versa to Tbilisi.
Airbnb is a great, inexpensive option for both Tbilisi and Yerevan, as well as Envoy Hostel, because they have locations in both cities, offer tours, and are well-versed in the local history and cultures of both countries. Bear in mind that there are not many 4 and 5 star hotels in either city. If you happen to visit during important events like the April 24th commemorations in Yerevan, airbnb. com is your best option for finding well appointed, reasonably priced accommodations for approx. $50USD per night.
