Well I think it all depends on what types of things you like to do. It also depends on whether you want to stay in the U.S. or travel outside of the country. I have traveled to several places here in the U.S. and I live in Vegas now which I think is a great place to visit. California and Colorado are also very nice places to check out. Although a lot of people travel as a couple to Europe but they also have some great place to visit there solo as well.
If you're traveling solo, you may want to go somewhere you can just relax and unwind by yourself (but without being totally lonely. Try a beach spot or a spa retreat. Otherwise, if you'd like to travel with people, but you just don't have anyone to travel with, find a travel group to go somewhere you've always wanted to see.
Do you like "disco disco"ing than you can try Alanya in Turkey. It is a small city with a lot of turists you can meet and make friends with. There are several beautiful beaches, too. After Sunset there are a lot of discos you can go to and you can go shopping for a little money :) hope it helped.
Places like Australia and New Zealand are very easy to travel around by yourself. I did them both last summer and felt very safe and as their english speaking, it's so easy to meet people. Happy travelling!