If the leak is new (haven't been seeing puddles before) and catastrophic, I would certainly check the hoses to/from the radiator first. The coolant could be everywhere because it's leaking near the fan and being sprayed.
Don't run the engine without coolant. You won't like the results. If you need to run it to see the source of the leak, fill the COOLED DOWN radiator and reservoir with water first. Don't take off the radiator cap while the engine is hot else you'll get a nasty, hot, boiling surprise.
good luck.