Tel Aviv is a very secular city. You wont have any problems finidng open restraunts and "Pitsusiot" (kiosks). But if youre not staying in the center or around you might want to stack up on smokes and other must-haves. Note that most places (except restraunts) close early on Friday and open Saturday eve.
Saturday night, one hour after sunset (the official end of Shabbat) everything comes back, full on! Buses are up and running, even more people are on the streets, with the Tayelet (Beach promenade) completely packed with families out for the evening stroll.
If you are staying in a hotel over Friday night (and just about every hotel other than hostels are likely to be kosher), kashrut rules will apply. The bigger hotels will have a Shabbat lift. Judeaism does not allow work on Shabbat and completing an electrical circuit is one such thing that is forbidden. Shabbat lifts are basically lifts that will stop at every floor, thus enabling observant Jews to use the lift - the pressing of a lift button would be completing a circuit. Ditto food - thus food that requires heating is prepared prior to Shabbat and kept warm throughout the time. Eggs, for example, can be boiled as long as the water they are boiled in is kept constantly hot. Coffee can be continually on offer as long as the machine requires no turning on and off (so once the coffee -or frozen margaritas on a hot day - runs out, thats it).
Unlike Jerusalem, there are no 'no go' areas for vehicles.
Yafo (Jaffa) is completely different as it is primarily (although by no means exclusively) Arab - either Christian or Moslim. Most things here are open throughout the day (huge queues form outside the famed Abulafia bakery on Yefet Street to buy freshly baked pitta and bread as well as borekas and Iraqi pizza).
As I already mentioned in my Israel page, as a Jewish state, religion is taken very seriously here. But more so in some places than others. Tel Aviv falls most definately into the 'others' category.
So what happens inTel Aviv on Shabbat? Effectively, for most, the weekend starts Thursday evening through to Saturday evening, with Sunday (as in the whole of Israel) being a normal working day (some people work Friday morning). As Friday sunset approaches, shops/markets will close as will kosher cafes and restaurants. Buses will stop running (although sheruts and taxis will continue to provide public transport). Many bars/ restuarants/ cafes remain open throughout, as will 'kiosks' (cigarettes, basic food stuffs etc). The streets tend to be quieter until later in the evening - many non-observant Jews continue the tradition of the family Friday evening meal. Consequently many bars and restaurants tend to be fairly empty until approx 10pm, when suddenly the city comes back to life. And remains so until the early hours of the morning (traffic jams at 4am are pretty normal!!). Saturday during the day can be blissfully quiet and relaxing - 8 months of the year it seems as if most of Tel Aviv is on the beach (with the rest either in cafes over very long brunches or just coffee or out and about at the major sites round Israel, BBQs in tow).
Its worth while knowing that everything closes down early afternoon friday for the sabbath until nightfall saturday. This means no buses or suppermarkets.So stock up in the supermarket and spend the Saturday on the beach. Night life carries on as normal, in fact friday is 'the night' for out on the town.