I agree with RedChili's post; West Jerusalem is very very safe in terms of street crime. If you can afford a 4-5* hotel during the holidays, you can certainly afford a very nice AirBnB in a posh, central neighborhood.
If by "security," OP means "terrorist threats" rather than pickpocketing, there's no reason to believe that there would be any sort of terrorist threat against AirBnBs.