How are we supposed to CURB OUR DOGS in Levittown....or other Nassau Co. communities?

Like 99% of my towns dog owners, I walk my little yorkie on the sidewalks on my block and a connected block.  Does CURBING YOU DOG mean you have to walk your dog IN THE STREET??  There are cars parked up and down our streets, so it's impossible to walk your dog next to a CURB for the length of the walk, and walking down the middle of the street doesn't seem very safe!  He also NEVER would pee or poop on cement!  Seems they are born to be grass, tree and hydrant pee and poopers!! I ALWAYS pick up after him when he poops...TOTALLY!!  Never leave a sign of any poop.  Am I breaking a town law by allowing him to poop on the grassy median between the street and sidewalk even if I completely clean it up?  It seems dogs, especially the males, will ONLY pee ONTO something!  A street light pole, a hydrant, a tree trunk!  He reads his "P-MAIL" left there by a previous dog-pal, and leaves an answer to be read by the next passer by!  PLEASE... tell me WHAT I need to do to be able to walk my little guy without breaking the rules!  There are some public lands around town where the signs just say  YOU MUST PICK UP AFTER YOUR DOG! These are areas where there are some grassy fields... but they are a DRIVE away.  Please help us understand the town rules.  Seems unreasonable as long as the area is totally cleaned up.  Thanks!!