Most runners train and race on the roads, thus the name for the sport of road running. When possible, run in low-traffic areas. Dodging cars is not fun. Run facing traffic so you can see cars coming at you in your lane and step aside if necessary. Flat roads are easier to run on than those with a high crown.
Many cities have parks with paths and sidewalks designated for endurance activities.
Plan to do at least some of your running on popular paths. The ideal running surface is smooth grass, such as on a golf course, but golfers often object to runners invading their turf. In an ideal world, we should be able to run anywhere at any time without fear of being assaulted. Our world is not ideal, so be careful where you train and when you train. If you have to run in the dark, or in unpatrolled areas, it's generally safer to do so in the morning rather than the evening.