If I were to secure my router by putting it in a plastic lockbox, would it dimish the wireless range of the router? I know a router can go through walls and floors, but I was wondering the implications of sticking it in a box.
Well you can place the router in a box to prevent it from stealing and still get the same quality of service. The idea is simple get a standard metal lockable electrical box (outdoor or indoor type), get a router with a detachable antenna then mount the antenna on the outside of the box, and connect an antenna to the router with the appropriate pigtail. Except the fact you are also worried about getting the antenna stolen too!
If that too worries you use an
ABS Plastic Box, they are invisible to WIFI routers so you can even place the antenna inside!
Any kind of physical interference whether a wall or box can affect the signal strength of your router. Depending on how thick and the material, it will vary on the range in which you will lose.
You're best bet is to try it out and see if it works. If you're experiencing issues, you may need to look into getting a repeater as well if securing the router(s) is your primary concern.