By central you mean the Tel Aviv area? How about Holon, nothing especially spiritual there, but there are some interesting museums and parks, like the Egged bus museum, many of which are very kid oriented, but an adult can enjoy them too.
There is Hertziliya and the marina there, Caesaria and the ancient port and a lot of old archeology (Roman in origin, though), Rehovot, which has a museum dedicated to the war of independence and the Weizmann Institute, which has a visitor’s center, and science museum. The outdoor things might not be such a good idea in this weather though.