Tel Aviv is the most modern and westernized place in Israel. Jerusalem is the official capital (although not internationally recognized as such) and the religiuos capital, Tel Aviv is the party capital (almost officialy recognized). When you walk the streets at night you can hardly imagine you are in the holy land.
Sidewalk cafes give the city a decidedly European flavor, expecially in the areas with Bauhaus buildings. Shopping at the enclosed Dizengoff Center is pleasant.
Tel Aviv is also the business center of Israel, and has the largest percentage of young people.
Jaffa is the old arabic part of Tel Aviv. It is much older (Tel Aviv was founded in 1909) and is now some sort of the Quartier Latin of the city. Although it has many small and trendy boutiques it still retains some of its flavour as an arabic city.
The best reason to come to Tel Aviv is to have a good time, the nightlife is great, there are good restaurants, there are so many shops, the beaches aren't bad and there is always something going on.
A good place for trendy shopping would be Sheinkin street; Kikar Hamedina is known for its upscale (and expensive) shops; and Azriely center, Ramat Aviv mall and Dizengoff center would answer all your shopping mall needs. Alternatively, you can check out Shuk HaCarmel, a large street market held daily on Carmel St.
Bazel and Rotschild streets have the best coffee places; Allenby, Lilienblum streets and the Tel Aviv port is where you'll find all night parties and bars; and you shouldn't miss the beach - for sunbathing and babe watching.