From a buyers prospective having a patio would be a strong factor when making a decision. Years ago we made an offer on a house that was smaller but had an amazing back yard with a pergola. It was worth the smaller rooms. Never did get that house. Turned out we weren't the only buyers interested. We went with choice two that was bigger, and still had a beautiful backyard but no pergola. We spent $6,000 to get that pergola on house two.
Won't get our money back but it was worth it. People love it and we easily rent out that property now that we no longer live in it.