MY 1999 HONDA ACCORD WATER AND COOLANT DISAPPERING

This usually indicates that you have a leak but check your oil to make sure your oil doesn't look "Milky" this would be a blown head gasket or cracked head and that's a whole other animal.
Alternatively you may also have a bad thermostat but, seeing that you did not include that the car was shutting of, this may not be the problem.
A leak my not necessarily be in the radiator, it may be in the hoses connected to your cooling system or in worst case scenario, you heating coils which run under the dash and is a very costly repart unless you decide that you don't need a heater in your car. Then you could possibly seal those hoses off.
You may want to run the car for a while and let it heat up. then, open the hood and look for steam and water drops. Also, keep your nose open for a sort of sweaty smell, this will be the water/coolant evaporating. you could oslo drive the car over some area like you white concrete driveway of someplace similar after a few minutes back the car off and see if you find water drops. If none of these work, you can also try turning on the heater while the car is nice and warm and try to see if you can smell that sweaty smell, this would be the heating coil.

First, check your oil and look to see if it looks "milky." If it does, coolant is getting into your oil, probably from a bad head gasket, intake gasket, or a crack in either assembly. Or... a small leak can be difficult to find because it will only leak while under pressure when hot, and it may burn off from the heat of the engine. You should put on a pressure gauge where the cap goes on and pump it up to the rating of your radiator cap and start looking for a coolant drip. (Do this with the engine off)

Check for any leaks on the outside of the engine. If there are no external leaks then you should check for coolant being burnt in the engine due to a head gasket or cracked engine component.