nighthawk x10 is the only router I have seen with plex built in.
all that said, I wouldn’t trust a router or drobo for a plex server.
an nvidia shield might be a solution, it can run as both client and server with local and/or remote storage (ie using the drobo for media storage). this is probably the simplest and best option for a small plex library. not necessarily the cheapest, nor the best for larger libraries.
another option might be an older model NUC you can pick up on amazon for cheap. you would still need an OS and be able to manage that along with plex and any other apps/services on it.