Can I encrypt user input in a way I can't decrypt it for a certain period of time?
This is an interesting discussion of the problem, as well as this crypto.SE question (they seem to be called "time-lock puzzles").

The most reliable scheme is to use a trusted third party which provides a public key and only releases the private key some time later.

The only scheme that doesn't require a trusted third party is to iteratively hash a random value for the time period you want, use the result to encrypt the information, and then discard the result and store the initial random value. To decrypt the data the iterative hashing needs to be performed again in order to recover the result which was used to encrypt the data, which should take the same amount of time it did before (although hashing can be sped up with GPUs or ASICs).