Do you have Drywall? No way to run cables up through the wall and then drop it down to the projector? I would do that for the cable box, and Room PC (if you have one).
For simplicity and budget sake, you can use an auto-switcher for the different sources, or, like Comix mentioned, can use a full Crestron control solution to control the different sources in the room.
For connecting laptops as people come in for their meetings, there are a bunch of wireless options to avoid the HDMI cubbies in the table:
Barco's Clickshare is an incredibly popular product that I sell a ton of:
https://www.barco.com/en/clickshare
Other options for Enterprise-grade wireless screen sharing:
WePresent with HDMI dongle (note - you need a separate power source for the dongle):
http://www.wepresentwifi.com/wipg2000.html - this is cheaper than ClickShare but also no good if you want to stream video.
Crestron AirMedia:
http://www.crestron.com/microsites/a...-presentations
Christie Brio:
https://www.christiedigital.com/en-u...ration-systems
If you have any other questions/need any help feel free to ask me