depends on which part of Jerusalem we're talking about. Most parts are very safe indeed, but two exceptions that I know of are:
1. East Jerusalem, where Palestinians dwell. If you're a tourist, they should be OK with you (and even welcoming), unless you are dressed in an exceptionally provocative manner. Plus, there are some violent protests over there once in a while.
2. Me'ah She'arim - a Haredi (ultra-orthodox) neighborhood. Similarly to the former example, it should be safe unless you are dressed provocatively. But you should also avoid driving through this neighborhood on Sabbath, as people (usually kids) would occasionally throw stones at vehicles that do so.