<map lat='54.689386' lng='25.280024' zoom='11' view='3' height='350' float='right' country='Lithuania'/> Vilnius is the capital of Lithuania.
When coming from Kaunas ask the driver politely if they drive near the place of your destination. If the answer is negative, it might be more convenient to take a free bus from a huge hypermarket called "Maxima" which is situated ~13 kilometres away from Vilnius (map) to the city centre or to some other destinations in the city.
North towards Utena A14
You can take a routing bus from Kunigo Broniaus Laurinavičiaus stop towards Raudondvaris. There is a good hitchhiking spot with bus stop and big cafe.
A hitch-hiking spot towards Riga (as well as towards Panevėžys and Šiauliai) is situated behind the bus stop after one of the major street crossings in Pašilaičiai/Fabijoniškės at pretty much the end of the Ukmergės avenue (map). There are many buses going this direction (you can use this journey planner) so you won't have troubles of getting to so called Via Baltica road (E67). Bus stop Bukiškių st has a bit more space after it for cars to stop. It is also a popular spot for locals to hitch-hike to their homes in towns nearby, so the smart thing would be to go a little bit further and to write your destination on a hard paper to show to the drivers.
Take the trolleybus 11, 16 (goes from main station) or 19 direction Pašilaičiai and leave it on the last bus stop Pašilaičių žiedas (point A on the map) and walk around 20 minutes by foot following the route on the map until you will reach point B. Cars don't go fast here because of the lights and there's enough place for car to stop.
There are two places in Vilnius offering you a good possibility to get a ride towards Poland. In order to get to Poland you can head towards Kaunas, Alytus (map) or via Trakai and Prienai (map). The three routes have ups and downs. Going through Kaunas is a longer road, but it's a highway and you are likely to need to change car only once in Kaunas and then in Marijampole, also it's a higher traffic.. the downside is that you are quite likely to get stuck in Kaunas since most cars won't go to Marimapole / Poland. Going through Trakai is recommended since all the cars that actually go to Marijampole - take this route (you might want to check what part of week or day you are going.. most cars go in the morning and after work, Friday and Sunday is high traffic too). Some Polish trucks go through Alytus from Minskas, so that might as well be very good option too.
Next to the huge shopping mall "Maxima Baze" Savanorių pr. 247 which lies outside the city. You can get there by taking a free bus run by "Maxima" every hour, at **:18 from "Savanorių", or from the centre of the city (info is in the spot description) schedule on the carrier website ("darbo dienomis" = Mon-Fri). Or, from the bus stop "Savanorių" on the Savanorių avenue take a bus 21, 22, 23, 29, 54 or trolleybus 4,6,11,12,14,16. To reach Savanorių from Main Station take Trolleybus 6. (Every 5-10 minutes).
Once you are there  walk east to the junction along the motorway or parallel Pirkliu street > Kirtimų gatve. Then go under the bridge and go up just after you cross it – there should be stairs just next to the bridge. It will take not more than 10 min. Then go to the parking opposite to "Maxima Baze" there you will see a parking space which is a perfect spot for the cars to stop while you are thumbing on the road. Google Maps shows Krims Keeabs there. This place has never failed, and waiting times are always good.
Note The fastest optiomn is to take bus Nr. 29 at Savanorių bus stop towards Grigiškės get out at huge bus stop Gariūnai and walk direction to motorway A1 to same parking
Note The middle of the motorway is upgraded with fence net and is 1,5-2 m high now.
At the end of Savanorių avenue (see the map, picture on the right), many buses and trolleybuses go there - it is easy to get there but the waiting time can be longer in comparison with the first described spot - it is mostly because of 2 reasons: less traffic towards Kaunas (since it is a road towards Alytus and Trakai, too), and competition (there wouldn't be a day without some local short-distance hitch-hiker standing and thumbing there).
This point is popular by hitch-hikers coming from northern part of Vilnius. There are free bus which takes you almost to the A1 highway, to the biggest market in Lithuania, "Gariūnai".Departure station. Schedule on the carrier website. Bus don't run on Monday.
After you get on the Minsk Road (Minsko plentas in Lithuanian, see the map) you'll see a huge supermarket on your right. You might as well look for Belorussians at the parking lot by this shopping mall - it is possible to convince some of them to take you to the border. If this doesn't work, walk about 50 meters ahead where the last slip road ends and a soft verge starts, and start thumbing there.
Take the bus 16 from train station (Stotis), the ride will take around 20 minuts. Leave the bus at Posūkis bus stop (it's just 50 meters before the bridge under the road, pay attention because it's optional stop). Walk 100 meters and hitch-hike after the junction. There is less local traffic here.
Note that it is no longer permitted to cross the border on foot, so be sure to get a lift across.
Adults: single-ticket only on-board EUR 1.00. If you plan to stay longer it is good idea to buy E-ticket card (EUR 1.50) and top-it-up with money or tickets. E-ticket prices: 30min - EUR 0.64, 60min - EUR 0.93. In ticket validity time you can change as much vehicles as needed. Students: get a 50% discount. You must have a valid student or school ID. ISIC must be used with your personal ID or passport.
Every bus has a machine to punch holes into the ticket which are shaped in a certain pattern (saying - there's no time limit on the tickets). People often leave there used tickets on the seat or drop it on the floor, so just take one and be happy. Alternatively always have a fresh ticket with you and punch it as soon as you see the controllers from the distance (they have a separate minibus and are usually 5 or more in shiny uniforms - easy to spot) - that said, it rarely happens that there are single controllers or conductors teams consisting of two people. You could technically spot them as well though. (Minibuses aren't so common in Vilnius and usually more expensive than the buses/trolleys.)