I'm thinking to go ahead and install 5, 6X6 treated posts, which will support a canopy with metal roof. End result, a nice sitting area with a bunch of rocking chairs and maybe some string lighting. Should be able to get it done for $2.5k.
I'm thinking that's an upgrade project for when you've proven that this venue project is a success. The roof is entirely unnecessary and rocking chairs are terrible for social events... to me it sounds like you're building a Cracker Barrel replica. In reality you're just creating the smoking section. Either way, nobody's going to not book you because you don't have a covered patio with rocking chairs.
There's probably some things on your punch list that are needed more than that (from that photo alone, I'd suggest some sort of flashing on the corners of the barn to hide those gaps).