A problem that is computable yet doesn't lie in NP?
The time hierarchy theorem says that, if you allow more time, you can solve more problems. It's normally stated for deterministic machines but it applies to nondeterministic ones, too. In particular, nondeterministic Turing machines running in exponential time can solve problems that no polynomial-time NTM can. NTMs running in doubly-exponential time can solve even more, and so on for triply-exponential, quadruply-exponential and so on.

So you need to investigate the class NEXP, and find some problems in there that are known not to be in NP.