You have a very classy-looking place. It would be a shame to klutz it up with a poorly-designed patio cover. If it were mine, I'd be strongly tempted to install a free-standing pergola-type roof over it (cantilevered over the house's soffit areas), with heavy white framing, such that it would make a statement in its own right and not compromise the classic look of the house. The downfall of that idea is the fact that you'd either need rain gutters installed on the fascias, or install custom swale-type diverters on the roof, above where the pergola would extend over. I'd also make sure the patio cover had several large skylites in it, to prevent making "dungeons" out of the sunny rooms you now have.
If you want to go "whole hog" and completely redo the rear roof line to accommodate the patio cover, that chimney (wood-framed, with steel flue) looks like it would be quite simple to extend vertically. Meaning it shouldn't deter you from going that route should you desire.