Usually look at sites for companies in your area that do race management and timing. There are a couple national ones but mostly for longer races, such as: half2run.com for half marathons and marathonguide.com for marathons. There are several sites that let you map a run. Google maps can do it, I thimk, and mapmyrun.com is perhaps best known.
Depending on where you live, there may also be local or regional websites with detailed race listings. For example, here in Southern California we have Raceplace, which covers the entire area from Santa Barbara to San Diego and everything in between, http://www.raceplace.com
@ 5K: Angels Baseball Foundation 5K, Anaheim, CA, 24:15
Friends of the Villa Park Library 5K, Villa Park, CA, 24:10
Coronado Independence Day 5K, Coronado, CA, 24:36
@ 10K: Great Race of Agoura - Old Agoura 10K, Agoura Hills, CA, 50:31