You don't need membership in an expensive club. You don't need a playing field. Step out your front door, and you've found your first running arena. Most runners begin by running around the block or down the street. Only later, do they seek varied locations for their running activities.
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.