Find a busy coffee shop that you feel comfortable in, and take up a space near the main door.
Avoid bringing anything to distract yourself with if you can manage it, although this may be more difficult for some than for others.
These are both valid points, but neither are reasons to not try out some of these places to meet singles on your own.
Perhaps a change of venue or attitude will make all the difference, but without trying you'll never know.
A note for heterosexual ladies: attending a sporting event with other single friends will surely net you a conversation with a stranger if nothing else since single women are usually in short supply.
Whether you are taking a couple of courses to upgrade, are a full-time university student or are passionate about tole painting, every community both large and small have courses you can take that will not only net you more knowledge but a whole new set of people to meet and interact with.
Another idea would be to contact national organizations overseeing smaller local chapters to see if they are planning any speaking engagements or are looking to start a chapter in your area.
By opening yourself up and making eye contact with all of the other patrons, you are also making yourself available to anything that comes your way, which could be a recommendation for a new book to read, a compliment about something you're wearing, or maybe even a date. Someone doesn't say hi back, and another person walks through the door ten seconds later.
You've lost nothing in the process, and potentially get to socialize in a lighthearted manner.
The point is this: try not to involve yourself into something so completely that you send off ' I'm busy' vibes.
You want to seem approachable, and hiding behind a laptop or book doesn't help!