VIA Spacing for RF and Highspeed Designs

A good rule of thumb is 1/8 wavelength of the highest frequency of interest.

"In RF design we typically need to work with only the fundamental frequency of operation. For instance: In a 2.4-GHz RF design the goal is to have a nice 2.4-GHz sine wave on our board with low harmonics. The frequencies that we need to be concerned with are really 2.4 GHz.

In digital design, the goal is to have a nice square wave on our board. A 1GHz digital data signal needs to be square for a good eye diagram. This means that the true operating bandwidth of these traces needs to be at least five times the fundamental frequency or 5GHz. This is from the rule of thumb that for a good-quality digital signal you need to pass at least the 5^th harmonic of that signal."

Source: Steve Hageman Via spacing on high-performance PCBs - EDN