I like white oak tavern for something close by. Still by the parking lot but the other side is trees, so get a table towards the back. Not a lot of great nature based outdoor dining right in the area that I can think of. I’ve always wanted to stop by Woodstock Inn.

Not what you were asking… But if you want a cool spot for beer check out Elder Pine. A bit of a drive but their outdoor area is spectacular. You can check their Facebook or website for food trucks. Most importantly their beer is top notch if you’re not familiar with it.