A little structure makes a patio feel like an outdoor room. Consider a paved or loose-stone floor, and use the house or a fence for a sidewall or two and a pergola or tree boughs for a "roof."
A pergola offers sun protection without blocking breezes, while its open sides frame the view and establish a sense of enclosure. This pergola was custom-made, but DIYers can build one from a kit.
Similar to shown:
Outdoor Living Today Breeze Cedar 8-by-10-foot Pergola, about $2,350; homedepot.com