There are plenty of good, solid, weather resistant patio storage boxes on the market. The only problem with them is that the more they contain, the more room they take up. This is why it may be a good idea to consider getting a storage bench. Not only does it do the job of storing things just as well as other boxes, but it doubles as a seating area, meaning that you save valuable patio space.
Outdoor storage bench:
Outdoor storage bench pictured: Keter 172255 105 Gallon XL Rattan Deck Box, sold by ivgStores.
Also of interest: Suncast Patio Seat, Mini / Suncast SSW1200 Mocha Resin Wicker 22-Gallon Storage Seat / Step2 Outdoor Storage Bench