You just need an empty box where the LAN cable comes out. Then put a keystone on the LAN cable, connect it to the access point with a short patch cable, and mount the access point on the box. Clean, simple, and better than using a socket... I have another question about your floor plan. The drywall between 3 and 7 is clear. Between the other rooms, are there no walls or like in the plan? With that size, you should at least have 2.4GHz coverage everywhere. The question is also how high your requirements are. I would probably work with two APs...