Public transportation is very good and inexpensive in Armenia. It can also be tough to get to more remote sites outside of populated areas. The system could be described as a hub and spoke system, with each city offering local transportation to its surrounding villages and each city offering connections to Yerevan. Most inter-city travel is by 14-seat minibuses or buses. Yerevan has a several bus interchange stations that serve the whole country, so depending on where you want to go, you should find out which bus interchange station services the area of your destination. Note, that unlike many countries in Eastern Europe, Armenian mini-buses do not sell tickets beforehand, and do not issue tickets at all. You simply pay the driver, at any point in the trip (though some will collect at the beginning). Exact change is never required, but a 20,000 note for a 1,000 dram ride might present a problem. Tips are unheard of on public transportation.
For the average western tourist, you can hire a taxi to go most anywhere in the country on very short notice. If you have decided to travel heavy by bringing big bags, then going by taxi will be the best option. Prices are about 100 drams (33 cents) a kilometer. Most taxis do not have meters though, so you should negotiate a price before you leave. Anyway, taxi is a good option in longer trips, especially if you don't like waiting a minibus for hours.
You can rent cars, but if you are used to driving in the West and have not driven outside of America, Western or Central Europe, you should hire a driver when you rent your car. Driving in Armenia for the average tourist can be a different undertaking. But if you decide to rent a car, there are a growing number of car rental companies, including SIXT (office at Zvartnots airport), Europacar, Hertz and others throughout the central Yerevan.
Most main roads around Yerevan are in decent to fair shape with some being in unusally good condition. When you travel north (Dilidjan) or south (Jermuk), roads are less maintained and rather bumpy and you can feel it especially when using public trabsport! (Minibuses are often in bad condition too) Pot holes are very much a part of the experience and can test your driving skills. Be careful and when renting an automobile, consider an all wheeled vehicle or sport utility if available.