Are there NP-Hard or NP-Complete problems that humans a really good at solving? It has been noted that humans are good at solving the travelling salesmen problem under certain constraints. Are there other NP-hard or NP-complete problems that human beings are good at solving? Has there been other research (psychological, neurobiological) on this?

One lead I'm currently investigating is how humans are good at playing Minesweeper, despite the fact that is it is NP-Complete.
With regard to the relationship between the brain and complexity theory, I think it's important to remember that the brain hardly ever comes up with exact solutions to problems and seems to prefer inductive reasoning to deduction. (How to induce a minesweeper strategy computationally) Furthermore, we mostly conjure up approximations. Précis of Bayesian Rationality: The Probabilistic Approach to Human Reasoning discusses problem solving in inexact (probabilistic) terms. I believe that one of the follow-up articles (Identifying the optimal response is not a necessary step toward explaining function, page 85) is relevant to your question:

"An explanation requiring an optimal response function must also
consider that: (e) for problems of inductive inference, the optimal
response is often analytically intractable to determine with exact
methods, and will not be unique; (f) behavioral responses are typically
approximately optimal, revealing a tendency rather than a
correspondence"