I have been to Egypt, most of Spain, France, Turkey, Amsterdam, Ibiza, the canary islands and the Balearic islands. I did most of these places alone and to be quite frank, it is more fun that way. Egypt was my favourite and I learned to Scuba Dive in the U.K before I got out there and it was a great experience over there. I also always wanted to see the pyramids and experience the culture. To date, it was the most interesting place I have visited. You meet so many people when you do it alone as you tend to mingle with people you meet. I recommend anywhere which has a whole different culture to the way of life you live in and are used to.
Don't go anywhere that is commercialised as a lot of these places are geared towards lager louts and don't offer much in the sense of experiencing a country for what it really is.
You might find it helpful speaking to a company like trailfinders in the U.K that offer some good advice on travel destinations and how to plan it all.
Trailfinders - The Travel Experts
The thing to remember about traveling alone is that spontaneity is the key to making it a memorable experience. You will also learn a lot more alone and perhaps even learn more about yourself too.
On the 8 hour coach journey from Sharm-el-sheikh to Cairo, I spent at least 2 of those hours in the on-board toilet and learned not to eat salad that has been washed in water my British *** isn't used to... LOL
Sorry, had to end it on that note.