If you want to discover other places than the center, you can go the Emek Ref'aim street. all the area are very quiet but this street moving a lot ! its more for family i mean, there have more restaurant than bars there. but you should walk and discover the area, on the day is really beautiful and you can go directly by feet to "Tahana Rishona " (First station).
Emek Refa'im St, Jerusalem, Israel