My input on this whole conversation:
Don't overfill your schedule!
This is not Alaska, or Antarctica, or any other tourist location where you can swoop in and snap some pictures and check it off the bucket list. This is a country with a beautiful Jewish culture that you will not find elsewhere in the world. While you could surely spend some time running around to the country's amazing sights and attractions, you should set aside some serious time to wander the neighborhoods of Yerushalayim.
If you would go to the Old City, I would say to spend a few hours at the Kosel and learn a seder in the churva shul. If you don't want to venture into that territory, spend a few afternoons walking Geula, Me'eh She'arim, or as @ushdadude wrote, spend a second seder at the Mir. Speak to local Yerushalmi's and get a feel for their way of life. You can walk away with a sense of mesiras nefesh for Yiddishkeit that you will not see anywhere in the world.
Note, I'm not referring to the Kedushah of the land, which is subject to your hashkafic understanding. What I'm stressing is the genre of Yidden and Yiddishkeit that exists there. It's not something you zoom through, but you stop, focus, think, and savor.
Just my thoughts. (Obviously.)
10000000%.
I plan on making a schedule of where I'll be when, and then a list of priorities for each area. If one thing takes a lot longer and doesn't allow time for another, awesome. Just means we're having a great time.
As far as J'lem, definitely plan on being there for Shabbos, which means Friday as well (shuk, just wandering about, etc.). I'm also leaning toward adding another day there - maybe the first one. I don't like the idea of finally arriving in Eretz Yisroel and just going to Rosh Hanikra. I feel like I should head straight to J'lem first.
So I'm thinking arrive Monday, overnight either TLV or J'lem. Tue do the Kosel, maybe
@satturn tour, and visit some family (is that too much on the first day???).
Wed-Thu TBD, and then Fri-Sha J'lem again.
Thoughts?