The phrase "avoid drinking" is correct and usable in written English.
For example, you could write: "Alcohol abuse can cause serious health problems, so it is important to avoid drinking."
Drink water one hour after meal, and avoid drinking cold drinks during meals.
Drink plenty of water, and avoid drinking coffee or soda before you kiss her.
They avoid drinking much water.
If you're pregnant or at risk for alcohol problems, you should avoid drinking altogether.
You should also avoid drinking alcohol for at least 24 hours before the test.
Still, she added, "women who are concerned about osteoporosis should avoid drinking cola regularly".
We both avoid drinking too much cow's milk, but the alternatives are rarely fresh.
"Pregnant women or women trying to conceive should avoid drinking alcohol," said Donaldson.
You should also avoid drinking alcohol while taking this medication.
Better yet, avoid drinking too much alcohol in social situations.
Try to avoid drinking too much pop/soda and avoid drinking too much coffee and don't smoke.
