Run a set of single wires, and remote switches.
Put a switch/router in the middle (or a side) of the ceiling, and run a small number of wires along the walls to switches on the floor near where you have clusters of people.Running from the cieling to the floor, you can follow the brick mortar lines (you'll get half on the mortar, half on the brick.. you can spray paint the half running over brick the same colour as the brick -- this will break the lines, and camouflage what you're doing.
Put the switches inside of pretty, wood cases... with or without locks, depending on how much you trust the staff to play nice.
Unless you've got dozens of people running video, gigabit backbone runs should be enough... run multiple ggabit lines to the central switches if you have to, single gigabit to the floor switches.
Generally, bandwidth use tends to be sporadic, so network congestion shouldn't be that bad .. There's rarely any real need to run single gigibit lines from the server room to every client. For most services, 100Meg should be enough to the clients (helps to moderate burst loads), and gigabit for trunking.