Eating and/or drinking is/are allowed on these premises.

I would use "and," just because "and/or" sounds to busy in the context of a notice. I would not use "is" or "are" in such a notice, seeing it as unnecessary.

I usually see: No Food or Drink Allowed.

Honestly, I've never see a sign giving permission for this activity.

But if it IS allowed, then I'd suggest

Food and Drinks allowed on these premises.

Not sure why; it just sounds better.

Thanks, Setanta and Punky.