We used this service twice this week, with our Dream AP it's free. The price listed outside the window is 2.50 for bags and 4.00 (it might have been 4.50) for suitcases. If you have a lot of bags it might be cheaper to use the train station as described by Lady&theTramp PLUS you'd get rid of them sooner and not have to take them through bag search.
There's one just to the right of the Guest Services window at the main park and one to the right of the ticket windows at the Studios. On the day that we tried to used the Studios storage they had a sign up re-directing to the main park. If you do use the main park service, you might be able to enter the park at the point, or if not, walk under the hotel to the main entrance (you don't have to walk back the way you came).
Obviously queueing can be an issue, but other than that it's a very quick and pleasant service. They didn't bat an eyelid when we went back and asked to put something else in the bag. Re the blanket and bag point, if the items are secured together there shouldn't be an issue, they may not want to take a blanket just sitting on top of a bag as they could get separated.
The main park window opens at 8am and closes at 7.45pm (when the park closes at 7pm - so I imagine that moves around according to the park closure times).