Cargo shorts (or any shorts that have pockets that can zip up or be buttoned), fanny packs, and windbreakers with pockets that zip up are the way to go.
I rarely have to experience the nasty locker situations unless it's Hulk. I've never been in the Gringotts locker rooms, but I've seen them. . . and it's always so tragic. Not as bad with Forbidden Journey though, that locker situation affects the actual queue of the attraction. Mummy's lockers are hideous, it baffles me that an attraction with a deserted indoor queue has to have outdoor lockers. Shorten the part of the queue that is never used, and put the lockers there