IMHO cabins 8390/8690 are the best... large balcony but sun and (some...) privacy as well. Cabins 1388/1688 more expensive (D1 instead of DA) and have a pole right in the middle (but they are larger... personally I wouldn't be interested in empty extra space). Cabins 7388/7688: no sun. Cabins 9390/9690 must be pretty good as well (they have a door + a porthole instead of a sliding door).
For pics of these aft cabins try my website http://www.voyager-class.com
Onboard pics-photo galleries-Aft cabins
PS: to answer your head question directly... the Royal suite of course...!