Where do cockroaches go in the daytime?
Basically, yes, cockroaches are very good at avoiding detection. Since you linked to the American cockroach (Periplaneta americana), I'll discuss that species in my answer. I've only twice, in my life, seen an actual cockroach. I don't know what parks you're referring to in your question or if it's that common. 

By the time you start lifting up a rock or board to look for a cockroach during the day, it will have already sensed you coming and have left. 


  They spend most of their time in narrow, tight cracks and spaces where surfaces touch them on both sides.
  (Cockroaches from the University of Minnesota)
  
  Cockroaches like to be touched.
  Roaches are thigmotropic, meaning they like feeling something solid in contact with their bodies, preferably on all sides. They seek out cracks and crevices, and will squeeze into spaces that offer them the comfort of a tight fit. And I do mean a tight fit. The small German cockroach can fit into a crack as thin as a dime, while the larger American cockroach will squeeze into a space no thicker than a quarter. 
  (10 Fascinating Facts About Cockroaches)


When you understand how thin a crack can be for a cockroach to wedge itself into, you get a better idea how they hide during daylight hours in the outdoors. Many trees have rough bark with enough crevices for them to hide. They could fit in the thin spaces between the bottom of concrete sidewalk pavers and soil, under leaf mulch and many other spaces you may never have noticed before. It takes very little. Best places to look for them in parks would be around trash receptacles where people toss food they didn't finish eating.