We know light can't escape a black hole but... Could light find itself in orbit around an object? Say the light is on the cusp of an event horizon. Could it end up in an orbit around the black hole if it was coming in from the perfect angle?
Yes, it is possible in the Schwarzschild solution, but the orbit is not stable. The radius at which this can happen is the photon sphere which lies at $3r_s/2$ where $r_s$ is the Scwharzschild radius. Photons which are at this radius may orbit, but the orbit is unstable in that if the photon moves any closer it will eventually spiral into the black hole and if the photon moves any further it will spiral out and escape.
Apparently there are 2 photon spheres for a rotating black hole, but I am not too familiar with those orbits. I don't believe they are stable orbits either.