Um, well, first of all. You cannot do Disney and Universal and Hollywood in LA in four days without a car.
You could stay in Hollywood/Universal city and take the red line to/from the other, but there is no direct service via train or bus to Anaheim for Disney. You should probably stick to either Hollywood/Universal OR Disney.
For safety I would stay at Universal rather than Hollywood. Or stay in any of the zillions of hotels and motels near Disneyland. I wouldn't recommend staying anywhere else in L.A. if your destinations are what you mentioned unless you are going to have a car.
In Universal city your two best bets are either the Sheraton Universal or the Universal Hilton. They are both right at Universal Studios. There are too many hotels near Disney. Simply do a search on travel booking site for hotels near Disney.