Thanks LAX_Esq and RedChili.
For various reasons I prefer not to drive, though it does sound like a good way to see more of the country - particularly outside the big cities. I will definitely look at the option of staying in Jerusalem for a couple of nights, and maybe even Acco instead of Haifa. It looks beautiful, so I'll definitely visit.
My flight arrives at 10.15am, so definitely still Shabbat. I found a 2-year old tripadvisor thread that says the Sherut runs to Haifa from Exit 2, terminal 3 for 119 NIS. Once I have chosen a hotel in Haifa/Acco, I'll check with them.
Thanks
Dr. PITUK