Since EE doesn't require the parent category to be in the URL in order to sort by category, your category URL titles can't be duplicates. The reason is, how would EE tell the difference between this URL for Category Parent 1:
http://mysite.com/cities/category/parks
And this URL for Category Parent 2:
http://mysite.com/cities/category/parks
As far as I'm aware, the only way to do this without hacking the core or using a custom field is to simply namespace each category:
- parent_1
- parent_1_parks
- parent_1_accomodations
- parent_1_dining
- parent_2
- parent_2_parks
- parent_2_accomodations
- parent_2_dining
Another option is to change how your categories are structured. So instead of duplicate categories, have separate category sub-groups:
Cities
Features
- Parks
- Accomodations
- Dining
Then the user picks the city, and the feature(s) to associate with the entry.