The bus company controlling the city is DAN, but there are other companies you can take.
Cost: 5.90 NIS
In case you're planning on having more than 5 trips on buses (within the city or in the centre of Israel), purchase a RAV KAV ticket from the driver (5 NIS). You can top up 30, 50 and 70 NIS on the Rav Kav, and get 25% extra. Topping up 30 NIS means you get 37.5, and 5.90 X 6 rides is 35.4.
You would find using BICYCLE is the easiest way to get to places inside the city. There are city bike you can rent called Tel-O-Fun, with bike stations everywhere.
Renting is between 17-23 NIS for 24 hours, for rides of up to 30 mins each. You have to wait 10 mins between every ride, but Tel Aviv is not too big, so everywhere is 30 mins away.