We did the Ramparts Walk yesterday.
No matter what the guide books tell you, you can only access the ramparts from Jaffa Gate. The books don't really make that clear. There are exits along the northern wall at Lion's Gate, New Gate, Damascus Gate, and Herodes' Gate. On the southern part the exits are at Zion Gate and Dung Gate - but the entrance is only at Jaffa Gate. The northern and southern parts are not connected, so it's kind of awkward if you want to go the entire way - you have to go north or south, then double back to Jaffa Gate and walk the other part. Also, the bits around the Temple Mount are closed, unfortunately, and the northern walk is closed on Fridays.
We decided to walk the southern part because we wanted to visit the Temple Mount afterwards. Since our initial plan to walk from Damascus Gate all the way to Dung's Gate didn't work out (see above), we walked the nice path along the outside of the wall to Jaffa Gate. Grassy patches where Israeli kids played soccer, some odd art installations, great views of the city, the tracks of the Light Rail close by (if you have boys, that's a definite plus), and bit and pieces where the kids can walk on low walls.
Jaffa Gate is very busy. It's a challenge to cross the street as traffic just rolls in through the gate. For someone like me who thought the Old City was off limits to cars, that was a surprise. Now, if you want to do the Rampart's Walk, the access to the Northern Part is right inside the gate on your left. There is good signage there. The access to the southern part is a bit hidden - you have to walk out of Jaffa Gate around the Tower of David (which made David giggle in delight) and the museum - there the access around the corner. You pay a staggering amount of money -- but the nice gentleman only counted two of my kids - then you climb two floors' worth of steps and arrive at the ramparts.
Two words of warning: on large stretches, your kids won't be seeing much as the walls are quite high. That also means they won't fall over, so that's good. However, the stones are extremely slippery. Thousands of years of trotting people have given the stones a very nice sheen - not a good thing when you climb down the really steep steps. Leah fell twice, and I slipped three times. I'm especially anxious about falling as I carry the expensive camera around. We didn't get hurt but if you are not a good walker, don't go to the ramparts.
But other than that, it's fantastic and something everybody should do. You get the best views of the city, of the Armenian quarter (complete with Armenian flags which was a funny sight to me), of the Church of Dormition, you can see as far as the Jordanian mountains, you see the Mount of Olives with all the tourist busses, and the Temple Mount. It's a fantastic walk.
We left at the Dung Gate and doubled back to the playground the kids had spied from the walls. And then we went to the Temple Mount but that deserves a post in its own right.