Magnetic equivalent of a pointy edge at a voltage A pointy edge set at a given electric voltage will usually induce localized but high potential gradients, hence high electric fields.
Is there something equivalent for magnetic fields? A simple geometric/electromagnetic configuration that can create large but localized magnetic fields/vector potential gradients?
 A: "Is there something equivalent for magnetic fields?"
It cannot be precisely equivalent because the "point effect" originates from the re-distribution of electrical charges.
"A simple geometric/electromagnetic configuration that can create large but localized magnetic fields/vector potential gradients?"
Yes, magnetic fields "prefer to travel through" materials that have high magnetic permeabilities. This allows creating strong but localized magnetic fields.
An example/application of this can be found in "flux concentrators" (look at figure I took from google images). Here, they are used to direct the flux into a smaller area; which amplifies the field at the center. This technique is becoming a popular way to increase the sensitivity of atomic magnetometers.

A: While waiting for more interesting answers, I'll post what I think is the geometric equivalent of a pointy edge: 

A tapered spiral, but obviously with the spiral return back on the untapered end so that we have a closed loop while also contributing to the magnetic gradient
