Try looking in www.airbnb but be aware you may need to cater for yourselves. Locals people will be better than me at saying what few food options there are other than the hotels.
You will be hard pressed to find such a rate for a family of 4. I suggest looking on Booking.com to see what is available in that price range for that night(there is a feature allowing to limit the cost). Come bsck here with names, if you want an opinion. Are you leaving the night after your Tel Aviv stay?
Thank you for you reply.
which area should I look into?