The UAE. I'd see everything I could possibly see and immerse myself in the culture. Then I'd make a two- or three-day trip over to Qatar, and possibly stop by Saudi Arabia for a day.
If only it was longer than 7 days.
Dude, you would be locked away in prison for your perverted mind over there. So would I. Though, I would head to Oman with you. Tons of Sinbad legends from that country.
For me, I would go to Scotland. Get me a top of the line kilt, both formal, casual, and old traditional (you know, just wrap it, tuck it, and get going). I would visit the estate that I own land on. I would go around and have everyone address me Laird, because of that land on that estate. I would hit up Edinburgh and Aberdeen, especially visiting Medieval sites, and peruse through old Medieval documents. Then I would ask for a week more, and another one, etc., because there is no time in the world for me to do what I would want to do there.