I don’t think that the off-centeredness is the offender here, it’s the finish. If you created a finish that extends continuously to the corner, the whole thing would have a cleaner look. Do a search for “fireplace” and choose “midcentury” in the style filter. You’ll see a lot of off-center fireplaces that look great. You could also balance it by adding shelving, wood storage, etc. to the right side. See examples:

Hang a piece of art or a tv on the wall to the right of the fireplace to help balance the space. Arrange your furniture a couple of times to find what works best, allowing enough room for traffic. Then measure the floor area and buy an area rug which will extend under the front half all the seating pieces. That will ground the furniture arrangement. Add accessories and some more art.
The patio furniture really has nothing to do with the family room furniture. Just don’t block the sliding door with the table and chairs.