Tel Aviv is considered by many the capital of Israel, and the center of the vast Metropolitan which is built all over central Israel. It is also where all the foreign embassies are located, since they do not recognise Jerusalem as the capital of Israel.
Tel Aviv is also a very bad place to start a hitchiking trip. There is almost no good hitchhike spot in Tel Aviv itself, and your best bet is always to take the bus to the suburbs and try there - which is a pain on Shabbath, since there the public transport is very limited and more expensive.
To Haifa and the North
Hitchiking to Haifa and the North is not that bad at all. From the central bus station, or from the Arlozerov Terminal (Namir street), you can take a bus to either the Cinema City complex (on the main road, 5 min out of Tel Aviv), or further towards Yakum (also on the main road, but 20 min out of Tel aviv, after Herzalyia). In both cases you can start hitchhiking from the bus station you were just dropped in.
To the Cinema city complex take bus number 501/601/90 (8.7 NIS). To Yakum Junction take bus 601 (13.5NIS). From these stops you can hitchike easily north, from the same bus stop you just stepped off in. To Haifa try to get direct rides, as sometime drivers get off the highway where there is no good hitchiking spot. To Afula and Tiberias you will need to get a ride which turns right in Ceaseria Junction to Road 65 - If the driver continues till Haifa then you will not be able to get off in that junction.
To Beer Sheva, the Negev, Eilat, Egypt and Aqaba (Jordan)
Heading towards Beer Sheva, there is not really a good reason to go hitchike, as the bus fare from Tel Aviv is just 14.5NIS (3 Euro). But if you really search for the adventure, or you are heading southern, you can give it a try. Take bus 475 from Tel Aviv central bus station, and ask the driver for a ticket till "El-Al junction" (11.7 NIS). The bus will pass the "Airport offices", and the next station is where you should get off. From the bus station you just descended to, it is possible to hitchhike south towards Beer Sheva. You go south on Road 40#, don't take a ride which diverts from this road, and you will get to Beer Sheva. (The last few kms are considered road 406, so don't worry about it).
If you are heading southern towards the Negev, Eilat or Egypt, then it's recommended to take a bus till "Goral Junction", 10 km north of Beer Sheva. Take any bus to Beer Sheva, like line 370 from Arlozerov terminal, and ask the driver to go off in that junction. From there continue your journey on Road 40, and again do not divert from this road. If you don't find there any long-haul rides, ask the drivers to take you do "Hativat Ha-Negev" Junction, from which any ride south will be helpful. Road 40 continues approx. 200 km south, till you reach "Ketura" junction, where you change to road 90 that goes all the way south to Eilat, The Jordanian border and the Taba border crossing. For the Jordanian border go off in Eilot junction and walk the 1km till the border, for the Egyptian border take bus 15 from Eilat (6.5 NIS).
guaka has had okay results with taking a local bus (Kavim 168 and some others) to the Tsomet Aluf Zede junction in Ramat Gan.
If someone offers a ride to Ben Gurion airport (the train ride cost 12.5NIS, and the bus to Jerusalem costs 18.5NIS) you can just take it, make sure to have a sign in English with Jerusalem and hitch at the terminal.
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Take a bus to the main bus station in Jerusalem. Go on walking further on Jaffa road, till you get to the main junction where you can see the "Begin" highway. Keep walking straight and pass this junction, and on your right (after the petrol station) you will see a bus station, the best spot to hitchhike according to many. Most likely you will see many other hitchhikers standing there too. If you get bored or want to burn some time, just behind you there is an ancient Palestinian village (Lifta), which was deserted in 1948. go down the stairs and find your way to the local spring.
Another option is to actually just wait at the first (busiest) petrol station. Signs work usually well here.
You could accept rides to Ben Gurion airport.