Be confident in who you are. Don't set out to impress, set out to give pleasure. If you're not used to fine restaurants, then don't choose one for your first date. Choose a place you know, or if you don't think that nice enough, go to a suitable restaurant and try it out with a mate first. Practise your manners, check out the menu, make sure you can afford it. People are awkward when they're out of their comfort zone.
They try to do something they can't really afford, something a bit above their usual style: awkwardness follows. Same as your folks. If they're not used to having people around, don't go there for your first date. If you have the right girl, she'll like what is usual for you. If not, you're not a good match.