I understand you wanting to place your first hide, especially with full family participation. And I also understand the difficulty of trying to find a "good" place to hide a cache in a saturated urban/suburban area (there are dozens of caches within a mile of where I'm sitting right now).
However, if you're having that much trouble finding a spot more than .1 mile from an existing cache in that park, why not go somewhere else for your first cache? Keystone posted that there are already 9 caches within 1/2 mile of your point... do you *really* need a 10th?
One or two caches in a small park, with maybe a few more in a large park, is more than sufficient. Too many caches in a small area just means that visitors can't find all of them in a reasonable time, or spend all their time looking for caches instead of enjoying the park... and isn't that one of the main reasons for geocaching? To find and enjoy new recreation areas?
J-Way