For those seeking to travel by train Israrail is ideal. Israeli trains are typically efficient and far-reaching. The views out the windows are spectacular, especially on Israel trains.
There are several railway stations in Tel-Aviv. Trains run to north all the way to Haifa, Acco and Naharia, south all the way to Beer Sheva and east all the way to Jerusalem. There is also a brand new railway to the new terminal at Ben Gurion airport and that is just real cool! Hop on the train in Tel-Aviv, whatever direction you want and enjoy not being in a bus!
My kids (boys age 3, 5 and 8) like the train so much more than riding a bus or even driving. Its a good thing to do with them, an outing unto itself.