The Gramercy Park, Union Square area of New York is on the east side from 1St. Avenue to Avenue of the Americas and from 14th to 34th streets, just north of the East Village and south of Midtown. Take a look at the map http://www.nycvisit.com/content/index.cfm?pagePkey=446
Since the distance from east to west is shorter than from north to south, that is the way I would walk, east to west and plot the path making use of the local parks for places to take a rest. Of course, there are plenty of restaurants where you can stop for a long cool drink and sit a breath also. The neighborhoods are a beautiful mix of old and new architecture, a pleasant place to take a walking tour just to look at the buildings, but try to get to see some of these attractions. They are some of the places that make New York a great place to visit and a very special walking tour of the Gramercy Park and Union Square area.
The Players Club
The Players Club is a private club located right opposite Gramercy Park, which is a private park not open to the public. The Players Club is one to add to your walking tour list just to be able to take a picture of the outside. They do have events open to the public, but they have a very strict dress code. Contact them if you would like to find out about what is going on when you visit.
Theodore Roosevelt Birthplace
The Birthplace of Theodore Roosevelt, the only President to be born in New York City is maintained by the federal park service and they conduct guided tours of the mansion. Check out the schedule on their site and contact them to be sure that they will be open on the day of your walking tour.
Madison Square Park
Madison Square Park is the site of the original Madison Square Garden that there is always something going on here. It is more than just a place to take a rest. Just look at the web site and see what is going on when you plan to have your walking tour. Try to block out a good deal of time for this one.
Union Square Park
Union Square Park is home to a year round farmers market where you can buy almost anything and everything. You can get the fixings here for a nice picnic lunch in one of the parks, on stop in at the restaurant right in the park.
The Flatiron Building is the oldest office building in New York City and at one time it was the tallest. There is a lot of history in the building and one you should at least stop and make a quick visit too on your walking tour.