WOW, a great view . Add plants. And Malibu lights instead. Yes wind could effect string lights. Add colorful pots with tall plants. A big bright umbrella. With some other patio furn. A L shape sect. With a couple of chairs. A fire pit . Treat it like another room. Desk wood is fine. Add color in pillows, n pots.

Yes clean and stain the deck. Since you are in the city, you would have to check building codes re: a fire element if that is something you are considering. You could also do rope lighting around the perimeter, large planters, tall grasses, tomato plants; don't know if there's a water source up there, take that into consideration-your local nursery should be able to help you. Bright umbrella or two depending on seating. It's a wonderful space, enjoy.

A nice water feature would be fun as well...and even better with a small "pond" like setting with a few fish in it.

Add something to give you shade. Love the idea of the pergola with a vine that would eventually cover.

I like the weathered wood but it might need protection to keep it lasting longer.