There's not much that can leak in the cooling system... heater core, radiator, water pump, freeze plugs, or hoses. I don't think your heater core is leaking, because it would leak inside the car and get your carpet all wet. If it's not leaking underneath the front bumper, then it must not be the radiator. You said you're pretty sure it's not the water pump, so that leaves either the freeze plugs or hoses. Although it may be possible that one of your freeze plugs are leaking, a leaking hose is more likely it, but you may have to take a closer look. I'm not sure why the coolant doesn't leak when it's running, and I thought so too with my car, but it ended up being that the coolant evaporated before it got the chance to hit the floor. Can you see any coolant leak trails underneath? The trail looks white if it got burned off. If so, try to follow the trail and find the source of the leak.
If you do end up replacing the hoses, get a hose clamp plier like this:
Those spring clamps are a PITA, and you can't even fit a regular plier up in the tight space underneath the intake manifold. Using this hose clamp plier will make your job a lot easier.