The most obvious way to hide things is with false walls/ceilings/floors. Assuming no one is using an x-ray hack, you can easily hide away a chest or two behind wood planks, which are easy to remove by hand, with a space open above the chest so you can open it without further destroying the area.
The best hiding place for such chests is in a ceiling, since few people will look up when trying to find your secret stash. If you build your home into a cave, simply build a roof, then place a chest above that roof and leave the area above it unmined.
For a secret chest less likely to be stumbled upon by entrepreneurial roof-builders, you can create walls in your building, and simply leave an empty space in one of your walls for a chest to be hidden in (a corner where four walls meet is ideal, since you can build two walls leading into the corner, leave a space open above it to access the chest, and not have any part of your secret stash revealed to a casual observer).
All of this of course is vulnerable to someone running in and tearing your entire building apart for your rare loot, so an Ender Chest is still the best place for incredibly rare materials. For slightly less rare materials though, this secret chest will do.