How can I concentrate points in areas of higher curvature?
The idea I would try to apply would be the following: I make the example for the curve, but it should be straightforward for the application for the surface.

Let's say we have a curve $\gamma$ uniformly parametrized. Let's say the parameter of the curve is $s$. Your goal is to sample point corresponding to value of $s$ such that the curvature is high.

If you get the magnitude of the curvature $c$, this will be function of $s$ too. So, if you normalize the function $|c|$, you will get a probability distribution. If you get the integral of such distribution, you will have the cumulative distribution. Let's call this cumulative function $C(s)$.

The sampling problem from a distribution given by the cumulative function is well known, so basically once you have sampled a set of value $s_0,s_1,\dots,s_n$, such value will be related to the points of interest.

The application of this method to the case of surface should be straight, since basically you have a two dimensional cumulative distribution function, but the sampling problem is exactly the same.

Just to give some detail, it is basically sampling from a distribution given the cumulative function involves two steps:


take a random value in the interval $[0,1]$, let's say $k$ 
solve the equation $C(s) = k$.


This approach is exact, of course it is expensive, but if you like such approach you can work on optimization.