Yep, if it were me, being cheap and in need of exercise, I would walk down to Wilshire from the hotel, take the bus down Wilshire to the Metro station and then train it to Disney Hall. Cost, around three bucks roundtrip, plus a walk through a beautiful area. BH is very safe to walk around, even at night, unless the BHPD harasses you for being a pedestrian (getting less common). Keep in mind it is not always so easy to hail a cab in the L.A. area. You can certainly get one at the hotel featured in "Pretty Woman" which is on Wilshire (forget the name). Maybe you'll see Julia there.
By the way, if you rent a car, parking in Disney Hall area is around $10, although often you can find street parking for free at night.