Definitely visit the wailing wall - there really is something there. Yad Vashem is a must too. Haven't been to Latrun yet, but I will in October - and yes its open to non Israelis, all museums are. I found them a freindly, hospitable bunch. Get in touch with some of the Israeli posters here and get them out for a coffee or a beer.
Like any place that you're going to be in for a while, grab a day sack, guide book, camera, sunscreen and water and go walkabout, get involved with the locals, visit a few bars, grab a coffee and falafel - dont spend all your evenings indoors. Education isn't just learning.