I love going to Hong Kong, Shanghai and Beijing by myself and find that I get a lot more done when I'm on my own there.
I second the vote for big cities on your own. My favorite solo destinations are in China. I love going to Hong Kong, Shanghai and Beijing by myself and find that I get a lot more done when I'm on my own there. Outside the big cities, I prefer taking a group tour, sometimes for security but mostly because it's more efficient. As for other countries, I'd love to go to Morocco, Egypt, Jordan and Dubai but would only consider a tour at least the first time. I'm not sure I'd feel totally comfortable on my own in the Middle East and North Africa.