If you do go out to a resturant, when the wait person asks if anyone would like something to drink before ordering, speak right up and order a root beer or something non-alcoholic. This will establish confidence with your family that your not drinking. Also, you'll have something you will enjoy that's non-alcoholic, which for me makes not wanting an alcoholic drink easier.
Go and have fun. Families, generally, are supportive of each others successes.