I would say getting ducks or geese is probably not a good idea in your situation. They would have a 10' x 15' area destroyed in no time. You would have bare dirt in the summer and a mud hole in the winter.
Have you looked into getting a couple bantam chicken hens (I don't remember if you had a reason for getting ducks instead of chickens)? I have tiny Serama chickens and they make great pets, especially for kids. They generally weigh less than 1 lb and are easily tamed and easy to handle. I am not really a chicken person as much as a waterfowl person (love my ducks and geese) - I got the Seramas for my daughter - but I've really fallen in love with them.
Here are a couple pics of my Seramas. They come in every color imaginable. I wish there was something (other than that dandelion) in the pictures for scale. That black & white mottled hen is only about as tall as a pop can.
I would only want to have the ducks as a pet. I don't really want to annoy the neighbors because I don't want them to feel like they are stuck next to a farm. I am sure their children would not get annoyed, but the adults may. Here in ny, our house is only about 7 feet away from our neighbors. Is that too little? I would strongly say our backyard is about 10 feet wide and 15 feet long. I guess I could open my options to having larger ducks or geese but then I can only have 1 or 2 maximum (which I don't mind). Our area is called Bayside Queens which is a pretty suburban area compared to other areas. We are only 45 minutes away from manhattan by car.