RBFs are splendid, but you don't need to have them "decay with distance", indeed, ones which don't (mutliquartics etc) often have better approximation properties and better-conditioned linear systems to solve, give them a go! https://www.sciencedirect.com/science/article/abs/pii/S09557...
Tbh, I tried several different functions, but nothing worked better than inverse quadric function. Though, I'm not sure if I tried anything without decay
One interesting group is the compactly supported RBFs, for example those of Wendland https://math.iit.edu/~fass/603_ch4.pdf the advantage being that the resulting linear systems are sparse, useful when you have lots of points to interpolate and "gaps" is not an issue.
Tbh, I tried several different functions, but nothing worked better than inverse quadric function. Though, I'm not sure if I tried anything without decay