Not all boxes are small... some are large enough to take a 3-ring binder. There aren't too many of the the big ones at most hotels but if they have them, you can use them. I have not had a problem keeping my box the rest of the day when I checkout. Just ask. Some casino-hotels have the safe deposit boxes in the casino cage rather than at the hotel front-desk.

Many of the modern hotels today are putting larger electronic-key safes in the rooms. Some of these are a cubic foot in size or larger. Sometimes a fee for their use... sometimes included in your room rate. The Tropicana has these in the tower used for convention rooms.

I was in Beau Rivage Casino/Hotel in Biloxi a few days ago and found my room safe was just sitting on a shelf... not bolted to anything. They have self contained batteries to operate the lock and an interior light so there is no need to wire it into a.c. power. The security dept wouldn't believe me until they came up and looked at it. They bolted it to the wall while I watched!