Speaking about the negev, on the way to Eilat there is a open wilderness area, something like a national park,
I think you mean Park Timnah (I may have the name a bit wrong). It is really nice but when I was there for an astronomy trip last summer they would not turn the lights off which rather frustrated a bunch of us astronomers who were there to enjoy dark skies.
If you like outdoor activities there is no shortage of things to do in Israel, and most are within a few hours drive of Tel Aviv or Jerusalem!