If you are driving on the 1st, you do NOT drink on the 31st! I won't; alcohol from NYE parties is heavy and will still be there at lunchtime on the 1st, when I want to drive.

Grape juice is a great option. Low alcohol wine/beer is OK. You can have a couple of 0.5% drinks and everyone can think they're full strength, just nurse them. Or go for grape juice. Or lemonade and orange juice.

I'm a drinker and I still love going for non-alcoholic drinks sometimes. Freshly squeezed orange juice is a great alternative because it's what you fancy at the time without screaming "not drinking!". I will often stop, think, then say "actually, do they have a cranberry J2O?", which isn't the same as saying "no alcohol thanks" but instead "I fancy a juice now."

I'd pour my own "grape juice in a wine glass" and nurse (or get your DH to do so), occasionally requesting a juice when others buy the rounds in. Nothing strange about the odd juice drink! Also, no harm in having 1-2 glasses of wine given to you. Give them to hubby after a couple of sips when he has finished his glass. Or just leave it on a table somewhere.