Tel Aviv is considered by many the Center of Israel, and the capital 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 nowhere you can hitchike from Tel Aviv itself, and your best bet is always to take the bus to the suburbs and try there.
To Haifa and the North
Hitchiking to Haifa is not that bad at all. From the central bus station, or from the Arlozerov Terminal (Namir street) take bus number 601 heading towards Netanya. Ask the driver for a ticket till Ha-sira junction (8.5NIS) or till Yakum Junction (13.5NIS) and get off in any of these junctions. From there 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 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 13.70NIS (3$). 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 hitchike 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, than ask the driver to take you down on "Goral Junction", 10 km north of Beer Sheva. 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.
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 hitchike. Most likely you will see other hitchikers 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.