In reply to Tall Clare:
There are millions and millions (I exaggerate only slightly) of 10K races all over the place. But do bear in mind that the races differ very much in atmosphere/level of competitiveness. The smaller (200-300 entrants) races are often filled with club runners and will be a much faster field than the larger (500+) events.
I have no idea how fast you run but if you are a slow beginner, the smaller races can be demoralising if you're not expecting it. As a slow runner, I'm learning to relish being at the back of the pack in smaller events - gives you plenty of space to run your own race. It's good for the soul.