Definitely spend a lot of time strolling through Chareidi neighborhoods. Malchai Yisrael on almost any day can make 13th Ave. look calm. Take the tunnel tour at the Kotel. You can safely take the #1 and #3 Egged buses to the Jewish gate of the Kotel that goes directly to the Kotel Plaza.
There are some great tours to Tzfas and Tiberas, we did Atzeret which is a frum tour. Visited lots of kevorim, although they do rush you a bit which makes a nice slow davening a bit challenging.
Stay out of East Jerusalem and the Arab quarter of the Old City. If you rent a car, don’t trust the GPS, since it doesn’t know political realities. Instead, have someone reliable map a safe route for you.
Most of all, enjoy the Holy Land. I didn’t get there the first time until well into adulthood and virtually kicked myself for not going sooner. It is a wonderful place, davening at the Kotel is so inspiring! And it’s also such a funny place, there’s always some sort of shtick going on, whether it’s the Nach nachs dancing on top of a van near the central bus station, crazy taxi drivers, or people who sit down at your table at a falafel place and start telling you a vaad. BTW, the falafel in Israel is phenominal, nothing like what we’re used to here. In fact, all the food is really good albeit the kashrus is confusing.