I am contemplating replacing the stock passive pickups on one of my guitars with a set of active ones, my only concern is where would the battery box go? Would I have to rout a space for it in the back of my guitar?
You could either make a hole for the battery.. or if you have enough space in the control cavity you can fit it there. The downside is that you need a screwdriver to change the battery (could be a pain if you're gigging).

It's a lot of work converting to active.. you pretty much have to rip everything out. I'd recommend getting some very high output passive pickups instead. Take a look at some Bareknuckles