1991 Honda Civic antifreeze leak

Everyday my honda loses abouy 1/2 cup of water/antifreeze from the radiator. There are no leaks in the hoses, no water visible underneath during the day or throughout the night (while parked). I just paid to have a new radiator put in, has new cap. It was suggested that maybe the water is going back into the head, but there doesn't appear to be any white smoke, no water in the oil. I have very depressed because with the high gas prices, I need to be able to drive the car further than to work (7 miles). Would like to take it out of town to visit my daughter and her family. My other car, Isuzu Rodeo eats too much gas. Any suggestions? I am very upset by this Janice