I'm not sailing on the Sun this month, but I was on her last month. My favorite lounge aboard the Sun is the Windjammer's Bar. Just next door is the Cigar Room, my second favorite place on board. Both are just aft of the Dazzle's Disco, and all three places are on Deck 6. You're just a short walk from the Promenade Deck.
Since the Sun is on a different itinerary from last month, I will not be much help with what to do off the Sun.
Enjoy your cruise. The Sun is a beautiful ship to spend a week or so aboard.