There are two main locations where we do speed training: the field and the track.
We're mainly talking about outdoor athletic fields in our case. However, many parks have fields that are fairly level and well manicured and thus also ideal for speed training. Natural grass fields are the most forgiving surfaces upon which we can run and train. You could say they are cushioned or shock absorbing (as long as they are not dried out and hard). The pros of grass fields is that they are great for change of direction work, easy on you if you slip/trip and fall, and usually a bit easier on the joints (at least in terms of impact loading). The cons are that these fields are seasonally-dependent, they require more "work" from your foot and lower leg tissues, and your times will be a bit slower than when on a track.
Speaking of the track, it's simply the best place to run fast. It's why the Olympics are run on the track. It's a measured, reliable surface which is level and free from holes, sprinkler heads, etc. It's firmer than grass but softer than asphault. You don't have to look where you are putting your feet because it's the same every time (this helps posture and form). Usually fenced off. No cars or pets to dodge. The venue of velocity. Tracks were made for speed. When you run a time on a track, it's universally meaningful. Not only can you run your fastest...you have legitimate data which is far superior that what you can get from any GPS watch. Once you're turned onto track and tuned into it...you won't need any convincing.
There's a middle ground (literally) which is an indoor or outdoor artificial turf field. These are often deliver the softness of a natural grass field with the consistency of the track. These facilities are great for training when you can access them.
Occasionally, in a pinch, you can use a quiet, level road for training. Just be sure it's not a high traffic area. I usually suggest you reduce volume by 20-30% in a session because the pounding is greater. I don't recommend using concrete roads or sidewalks at all. They are too hard and injury risk goes up exponentially. Firm sand at the beach is excellent at the beach when you can get it.
One last thing. In the U.S. it is conventional to describe distances on a grass football field in yards, while on a track they are in meters.