In looking at replacing my disc brake rotors, and looking online I see there are different sizes available (between 180 and 203 mm). My question is, what dimension do I measure on my existing rotor? I'm assuming it's the outside diameter, but just want to be sure.
Yep, it's the diameter. Most likey 160mm, but double check. You'll need to get the same size rotors as your old ones unless you get new adapters for your frame.
Note that the thickness of the rotors may differ slightly, so you may have to adjust the brake pads a bit. Also note the difference between bolted and center-lock rotors. Most likely you have a 160 mm 6-bolt rotor though.
You will need to replace your rotor with the same size as you already have. It is normally stamped on the rotor, the most common size is 160mm