Intra-city bus transportation is available both in Jerusalem and Tel Aviv.
The major company in Jerusalem is Egged. They have recently re-vamped their web-site to provide an on line search engine that provides both inter-city information and local information. The site is www.egged.co.il. They will provide bus line information and schedules but no maps. Once you are here you can make use of their text message or phone information service.
The major provider in Tel Aviv is Dan. They too have a website with a lot of useful information which also includes maps of individual routes as well as an over view map of all of Tel Aviv with bus routes. Their site is: www.dan.co.il.
Both sites are also available in English, however the information in English is not as comprehensive. Additional information is always available from the Ministry of Tourism information booths, one of which is at the airport when you land, as well as at the hotels.
Israel is waiting to welcome you with open arms.