OK, note that September 20 is to all intents and purposes another Shabbat, when there will be no public transport (as I already wrote). Everything in (Jewish) Jerusalem will be closed from the afternoon of Friday September 18 until after dark on Sunday September 20. There will be no intercity (or local) public transport on those days, with the exception of the sherut from Tel Aviv to Jerusalem, and taxis. This is what happens every Shabbat (Friday afternoon until after dark on Saturday), but this year Rosh Hashana falls on Saturday-Sunday, so it's two consecutive days.
So I would suggest one of two alternatives for that long weekend, in no particular order:
(a) Jerusalem, spent mainly in the Arab (east) part of the city, where everything will be open as normal. You will be able to walk around the Jewish Quarter of the Old City, including the Western Wall. But you won't be able to take buses to anywhere in west Jerusalem, and just about everything there - including restaurants and fast-food places - will be closed anyway.
(b) Tel Aviv, which is secular, and where almost everything (except banks etc.) will be open as usual, including of course the beach. I'm not suggesting you should spend your limited time on the beach though!
As to what to see in those cities, you've given no indication of your interests, but Google will provide plenty of suggestions.
While you're in Haifa, take the Carmelit (subway/underground railway) to the top station (Gan Ha'em), come out of the station, walk down Sha'ar Halevanon Street for a minute or so, then turn right onto Yefeh Nof Street, from where there is a wonderful view over the whole city. ("Yefeh Nof" means beautiful view or panorama.)
