Thanks everybody for suggestions... LM is $50/day more expensive compared to the Sheraton which would be hard to justify as I'll come to see a dead sea, not a hotel room.
I will have a rental car... so what would be the fastest way to get there? through Jerusalem (via HWY 1 and then 90 south) or through Be'er Sheva (40/25 west then 90 north)?
I understand that if I will drive through Be'er Sheva I will not be driving through West Bank area (which I would rather avoid giving options)?

AX