Here are some recommendations of must visit places in Jerusalem's New City.
Three Views of Jerusalem
To understand Jerusalem you should try and see it from the three important viewpoints – The Tayelet, Montefiore's Windmill & Viewpoint & if possible from Mount Scopus by the Hebrew University at the Tabachnik Park or better still from the Mount of Olives. Also stroll towards the other side of the mountain and enjoy the contrast of more than 3000 years of urban development with the raw desert. On a clear day you can see the Dead Sea in the distance. See Jonathan's Jerusalem Skylines
Yemin Moshe & Mishkenot Shananim (Windmill)
There were the first neighbourhoods built outside the Old City in the second half the 19th century. Now an artists colony and exclusive neighbourhood – so exclusive that there is an endless stream of tourists passing their front doors! Walk towards the French Consulate and explore the look out points in the park and along Paul Botta Street.