Is it safe to drink alcohol and take doxycycline hyc?

Yes.

There is a minimal risk of drinking alcohol while on doxycycline. Extended binge drinking has been known to increase the speed of elimination of doxycycline in the body.

From Drugs.com: Chronic alcohol consumption may enhance the elimination of doxycycline. The mechanism is induction of hepatic microsomal enzymes by alcohol. In one study, the half-life of doxycycline in six alcoholics was 10.5 hours, compared with 14.7 hours in six control patients.

So don't be worried about going out and having a few beers, just make sure its not a regular thing. And you are surely on medication for a reason, and since the drinking may decrease the effect of your medicine... you need to be cautious.

Be safe, and think before you drink.