Every outdoor AP(not repeater) will require a cable connection, typically in a large open outdoor area this requirement is impossible, that's why Mesh come out.
Another alternative to MESH is using bridge with wireless client, however this method can't provide a dynamic calculation on RF route, so that if for example one of the root bridge is dead, then the associated non-root bridge can't dynamicaly associate to an alternative nearby root bridge; While MESH can dynamicly determine the parent MAP which provide a redundancy in RF, for example, cisco use AWPP protocol among MAPs. That's why we say Mesh is more powerful in outdoor area when there's no fiber/cable resource
For a mesh solution, typically they will use 11a as backhaul, use 11b/g as client connection, to allow a full 11b/g coverage in a open outdoor area, typically there will need 25 Mesh APs per square mile(each MAP have a coverage distance of 600 feet)
In your case, since the park is very small, if you can only provide one fiber/cable to this area, then you have to use MESH, connect the cable to the RAP, use 11a as backhaul to connnect other MAPs(remember to limit the hop count as small as possible, one hop prefered, otherwise performance will sharply decreased when hop count increased).
If you can provide several fiber which can be placed around the rim of the park, you can also select to use outdoor AP plus directional antenna, but you need to carefully calculate the location and availability of the AP to provide a full RF coverage.
Other things like mounting place, power and anti-water/thunder accessories also need to take consideration.
