A rental car at Tel Aviv Airport costs 40 $ per day. For a week, you can explore Tel Aviv and Israel by car hire from Ben Gurion Airport for 277 $.
Plan enough buffer time for your onward flight. Depending on the selected refueling regulation, you must fill up your rental car accordingly before returning it. Have everything documented upon return in order to get your deposit refunded smoothly.
Cancellation is free of charge 24 hours before the start of the rental period during Driveboo opening hours.