Traveling alone is priceless.
There's no concern about leisure/taste differences in dining, entertainment and lodging.
It's cheaper. Enough said.
Less to worry about. If your spouse, friend, relative or whoever your travelling with gets sick, lost etc, it's a pain in the neck.
More flexibility. Do what you want, when you want.
Lastly, Privacy. If you like to do anything wild, crazy or border line well..

no one's watching you.
Places to visit. That's tough. I'd suggest Prague-Czech Republic, Dubai-UAE Johannesburg-South Africa, Mumbai-India, Amsterdam-Netherlands, Cancun-Mexico and Flourence-Italy.
Oh, and ofcourse, Las Vegas.

can't forget that.
Those are some of the places i've visited in the past and have had great experiences.