Haifa is very worth seeing, one of my favorite cities in the world. Elijah's cave is interesting if you are there, a site holy to Jews, particularly Sephardim (Jews from Middle Eastern and North African countries). Higher on the mountain is the Church of Stella Maris with a French Carmelite presence that dates back to the Crusader period, hence the name of the area, "French Carmel."
But please don't miss the magnificent city of Haifa if you visit. It's a lot more than Elijah's Cave.
Definitely visit Haifa, the Ba'hai Gardens and its many beautiful places.
I wouldn't go to see the Elijah Cave, its not that interesting, on the other hand touring Haifa going up to the university tower to the 30th floor and have a magnificant view on the North of Israel, visiting the Bahai Gardens (do not forget to make reservations at least 48 hours prior to the visit - phone 04-8313131) this I would certainly recommend.
I think Fugu12's main interest in visiting is religious pilgrimage sites, so I won't dismiss Elijah's cave. But both Anon and Betina are right that it would be a crime to visit Haifa and miss the view of the bay (which can be seen from Yefe Nof Road) and the Bahai Gardens, which can also be seen from that road. They are a modern wonder of the world, in my view.
You can do a really cool and not very difficult walk down from the Stella Maris monastery to Elijah's cave including a lookout on the cliff. Ask someone up at the top where to begin the walk. It's easy to get there from the bahai gardens (short taxi ride) so you can do both.
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