Yerevan is the capital of Armenia.
Hitchhiking out of town is pretty easy. Be careful of people who are actually taxis and want you to pay. But people stop relatively easily.
Take metro to the station "Sasuntsi David". Once you walk out of the station through the glass doors, you'll find yourself in an underground pass with many shops. Turn left and walk straight until you get out to the street. You'll see many buses and minibuses parked here. Ask for the bus that goes to the city of Vedi. Make sure to tell the driver to you need to get off the bus at the turn to Khor Virap. Usually, all the bus drivers know that if there are travelers in the bus, they're all headed to Khor Virap, so they'll stop at that turn anyway. When you get off the bus, you'll be anout 50 km from Yerevan already. The roadside here is wide, and the spot is very suitable for hitchhiking. The bus costs AMD 400 per person. (1 USD = 489 AMD as of February 2, 2016).
Actually, you can get off the bus anywhere even before getting to the Khor Virap. Once you're out of the Yerevan, just tell the driver to stop anywhere you feel is a good location for hitchhiking.
Another option is to take the bus going to Ararat from that same bus station, but you'll have to get out of the bus right when it gets to the main road. The bus turns left and goes to the city of Ararat by another road and you'll get stuck in the city. Another problem with this option is when you get off the bus you'll find yourself on a newly built road which has no suitable roadside.
From the city center, or Yeritasardakan metro station, walk along Abovyan Street in direction north. When you reach a roundabout, take the second exit to the motorway. You will see a huge bridge - go under it. Approximately 100 m behind it there is a nice hitchhiking spot, next to a bus stop that almost nobody uses. There is no pedestrian crossing in the vincinity, and the road is huge, so better to choose the right side of the road already at the roundabout.
Another option is the bus 259 (long blue bus that looks quite modern compared to other buses) leaving from Kilikia Central Bus Station to Abovyan. It takes about 20-25 minutes to get out the city. Tell the driver you need to get off as Northern Bus Station (Hyuseesayeen Avtokayan in Armenian). Walk 10-15 meters along the road until you find a suitable spot, and start hitchhiking. Bus fee: 200 AMD (~$0,45).
There is also a free bus from Kilikia Central Bus Station to Abovyan that follows the same route as the bus #259. But not knowing Armenian, it will be hard to find the bus, because it has an Armenian language sign saying it's a charity bus The sign in Armenian is: "ԲԱՐԵԳՈՐԾԱԿԱՆ ԵՐԹՈՒՂԻ ԵՐԵՎԱՆ ԱԲՈՎՅԱՆ". If you manage to find it, take this bus (usually old soviet buses colored orange - on wikipedia), get off at Northern bus station and hitchhike from there. Note that this is charity bus so you don't have to pay anything.
Take marshrutka no. 18, i.e. from France Square. After a while you'll pass some very ugly appartment blocks and then leave the city. This is the main road out of town, nice place to hitchhike. Make sure you get off right in time as the marshrutka will leave the main road for some villages.
update to Marshrutka 18 you can get it at France Square at the Marshal Baghramyan Avenue (north west street direction). It is like Marshrutka #57 yellow and cost 100 AMD (you pay when you go out) But I don't recommend to take it because it is just crossing M1 Gevorg Chaush Street once and than it is driving already in the wrong direction. The spot where to get out is difficult to realize, because #18 is driving often left and right turns and at the M1 road you are still in the block house naighberhood.
You can also take bus #57 (colored yellow). Pay attention, at one point you'll notice you're at the city limits. Get off the bus. You'll see the highway running North. Start hitchhiking after the petrol station. Bus fee: 100 AMD.
Update and recommendation for Marshrutka #18 and #57. I would recommend to take metro to the last stop Barekamutyun. The exit is bit complicated but when you are at the street you can orientate better. You must go to Kievyan street.(it's the street which is heading bit downhill) In the beginning you will see a bus stop where #18 and #57 is passing by. With Mashrutka #57 you realize that you are nearly out of town when the block house naighberhood is ending and you are driving north at M1 Gevorg Chaush Street. You are passing some gas stations and the street is uphill. Go out there. Straight forward you see the highway bridge where you can walk to the highway and stop a car quite quick.
Another option is from Kilikia Bus Station take a bus going to the city of Ashtarak. Tell the driver you need to get off at Bagavan. The bus will stop on the main road next to gas and petrol stations right before it enters the city of Ashtarak. You'll find yourself on the main road that goes to the cities of Gyumri or Vanadzor. The road splits about 2-3 kilometers after - going to the left towards Gyumri and to the right towards Vanadzor and Armenia-Georgia border. The bus costs 250 AMD. This location is very good for hitchhiking and in most of the cases you can hitch a direct ride to Gyumri or to Aparan (direction towards Vanadzor).
There are no actual tourist information centers in Yerevan, but free travel maps can be found in most of the hotels and hostels in the city. Travel information can be obtained at Hyur Service center.
There is also a small tourist information corner with free maps of Yerevan and Armenia in AEON anti-cafe. Some of their staff members are hitchhikers, so they can provide you with the required hitchhiking related information, or connect you with local hitchhikers. You can also get information on city and regional transportation, destinations, camping areas, as well as about events in Yerevan. Also, if you're a member of Couchsurfing, BeWelcome or TrustRoots, they offer to stay at the anti-cafe for half an hour free of charge. You can have tea, coffee, use their laptops/tablets to go online, or take a short rest before continuing your way. It may also be possible to leave the backpack at their storage room.
Pitching a tent can be done easily in the English Park (Angliakan aygee). It's very calm and safe. [Balkasus 2016] Sleeping with tent is also possible in Первая Перевалочная 
Using public transport is most of the times 100 AMD. In case of Bus/Mashrutka you pay when you go out of the Bus/Marshrutka. If you take the metro you buy an chip for 100 AMD. You don't need to buy an metro card.
About map's services. I didn't find any Application which shows me the Bus/ Mashrutka lines. Not Yandex Maps, not Goolge Maps, not Mapsme and not OSMand. So you have to ask locals.