As a few others have already said, if you plan to spend your time in Jerusalem, thats where your hotel should be
The neg about Jerusalem is AFAIK there are only 3 hotels where ones pts can be used both close to the entrance to the City and apx an hours walk to the Old City The Cronwe Plaza (part of IHG group) or The Ramada (part of Wyndham).The Waldorf (part of Hilton). While TelAviv has over a dz hotels where ones pts can be used.
That said I usually use
www.directrooms.com to find my hotel when in Jerusalem (4-5x a yr) If I wanted to be close to the Old City and not spend a fortune, Id stay at The Prima Kings rooms are small but in comparison to the other hotels in that area so is the rate. Theres also The Eldan Hotel, Dan Panorama. Havent stayed at these last 2
I wouldnt go with a car (although I always do) if I was in your shoes.
The Kings is a 10-15 min walk to The Old City, Mamilla Mall, Ben-Yehuda St for Sat night.
Now if clubbing is what you want then TA is the place to be and not Jeru
In regards to the Sherut to Jeru (only way to go IMO) at times they will wait till they fill up or get to close doing so, if not they will ask if everyone is willing to pay more so that the driver ends up with the same money as if it was full. Ive always said no and at time with just 2 or 3 people he still took us since he didnt want to wait the few hrs till the next flight would come in. Some times they would budge so I took a cab, so try 1st for the sherut but be prepared to take a taxi, god idea not to hang around and instead get out to teh stand ASAP to make sure you get a seat on what maybe the only van going(w/o knowing your carrier and arrival time cant know what will be)