I second the recommendation to at least flip through Gravitation. It has an intimidating size, but easygoing manner. I had a lot of difficulty with Spivak's Calculus on Manifolds (which has essentially no physical intuition outside the Archimedes exercise at the end), but I think I was uncomfortable with the abstract notions of tensor product and dual vector space at the time I was learning from it.
You might try Sternberg's Advanced Calculus (available on line), especially chapters 11 and 13.