@ross4,
The town's name is Aguas Calientes and it's a lot of fun, just like everything else around Cuzco.
Your itinerary is fine and doable although I have a few remarks:
The weekend isn't ideal for Jerusalem as less places are open (shops, museums, markets, mosques, synagogues, etc. All depending on the day and part of the city you're visiting).
According to your plan, thurs, sun, tues, and thurs will be mostly flying and driving so I've rearranged it a bit.
Unless there is some nighttime activity in Petra, I would spend only one night there,
Otherwise, the next day will be mostly wasted.
Same for your flight to Eilat- if you fly mid-day you won't get anything done in the morning and by the time you land in Eilat, cross the border and arrive in Petra, it'll be late afternoon and again- you won't see much.
Rent a car for 2 days and use is for one day in the north and one day in the Dead Sea area.
thurs - arrive 17-15. Sleep in tel aviv
fri – half day in tel aviv and fly tel aviv-eilat around 16:00, bus/taxi to petra or early morning flight to Eilat which may give some daylight time in Petra/Wadi Rum. Sleep in Petra.
sat – visit petra, fly eilat-tel aviv in the afternoon/evening. Sleep in tel aviv
sun – morning in tel aviv, noon- rent a car, drive to the north. Sleep in the north (many great options).
mon – A day in the north (haifa/gallilee/Nazareth), around 15:00, start driving through the Jordan Valley (Route 90) to the Dead Sea. Sleep at Metzoke Dragot, Ein Gedi or Masada.
tues – The dead sea area. In the afternoon- drive to Jerusalem and return car there. Sleep in Jerusalem.
wed – Jerusalem.
thurs – Jerusalem, until 14:00. Shuttle to the airport, fly home 18.15
friday- totally inefficient day at the office...