Mont of Olive to Jerusalem old town

Mount of Olives is close enough that you can walk up and down from the back of the old town. I would walk up though when it is still cool in the morning or evening. Some people like to take a taxi up and walk down. You can also catch a local bus up to the university on Mt Scopes and from there walk across the top of the hill through the small town that is on top of Mt of Olives and walk down from there...through the Jewish graveyard...takes a few hours to do that.

Thank's for replay.

Finaly it seems that we will sleep in Ain Kerem. According to my reaserch there is possibility to use Jerusalem local transportation to get to the city. Any tips how to do that every day?

If you’ll be using public transport in Jerusalem you should get Rav-Kav smartcards. These will save you money if you need transfer tickets, because transfers are available only with a Rav-Kav. You can buy the basic card for NIS 5 from the driver of any Jerusalem city bus. You then load it with “rides”. A “ride” costs NIS 6.90, and that gives you 90 minutes of unlimited travel on city buses and the light rail (trams). You can load two, 10 or 20 rides (nothing in between). Just tell the driver how many rides you want, and give him the money (cash only). He will then load the card for you. Then each time you get on a bus, place the Rav-Kav on the machine reader next to the driver.
For the trams, put the Rav-Kav on the machine reader just inside each door of the tram. Any passenger will show you how to do this.
If you don’t have a Rav-Kav you can buy a single ticket (not valid for a transfer) on the bus. For the light rail you buy single tickets in the machine on each light rail platform (there are instructions in English). You must then validate this paper ticket in the machine reader – again any passenger will show you how to do it.
Two or more people travelling together can share a Rav-Kav on the buses, but for the trams each person needs their own Rav-Kav.
There is no printed bus map for Jerusalem, but here is a link to one:
http://tinyurl.com/mcqpq2h
From Ein Kerem, you take bus 28 to Mount Herzl, and the tram from there to the city centre. Coming back, Mount Herzl is the last stop on the tram line, so you can't miss it!

Thank you very much. I didn't even expect so detailed information :)

We took bus number 75 from the Arab Bus station near Damascus gate which is going to the top of the mount (near Paternoster church) and walked down from there. From the bottom (Church of all Nations/Gethsemane...) it is a short steep climb to the old town (Lion's gate).