How do you determine which is the best next point where to evaluate the model?

Simulated annealing is blind, what you do with simulated annealing you just move locally around the current point.

If you had a partial picture of the landscape of the function, how would you locate the most interesting unvisited point in the landscape?

I do have to admit that what I'm seeing here is only the application of Bayesian sampling algorithms, there are startups doing similar things for A/B testing and similar.