You might be interested in "driveway":
- driveway
noun
A short road leading from a public road to a house or other building.
‘one of the suspects backed a vehicle into the driveway’
(Lexico)
The fact that you could park your car there makes me think of this. Also, driveways are often used recreationally. It's not uncommon for kids to play there, or for families to set up make-shift basketball courts on them, for example.
In AmE, at least for a small house (like the one pictured above), I imagine the yard to be a grassy area. See number 2 below.
Definition of yard
1 a : a small usually walled and often paved area open to the sky and adjacent to a building : court
b : the grounds of a building or group of buildings
2 : the grounds immediately surrounding a house that are usually covered with grass
(M-W)