A) You should not approach the offices without an appointment. You won't even get in the building. That includes the Sesame Offices, rough I know... But in these times it is a nessasary thing.
B) The Mansion, is just a building now, there is no indication that special place existed, just a hulk. Sad but true.
C) Kaufman-Astoria is outside walking distance - you should reconsider because it is a hike and you will be turned away.
Most of the Muppetty Goodness now resides in Kali-fornia at Chaplin Studios.
If you want to see some Muppet Sites:
The street that the Muppets march down and Kermit get's hit by a car is right next to Grand Central Station and 5th Ave. The old Biltmore supposedly. My wife works in that office occasionally so I know it by heart.
Bryant Park is just around the corner from there. Also a good Spiderman Site at the Central Library where Uncle Ben Dies and the Ghost Busters thing.
The Helmsley is a backdrop for some Muppetty stuff, But you need to stay down wind of the horse Urine!
On 5th Avenue - near the park is the World of Disney (555 5th) on the Second floor is a piece of artwork that used to reside in the Mansion stairwell. The Ballon Race - Has all kinds of Schielich figures. Really dusty, so I suggest distance pictures.
You could visit the Bridge in Central Park (Sesame and the Muppets used this site)
Times Square - There is the Naked Cowboy, TRU,MTV, ABC,NASDAQ,Bubba Gumps, all for tourists
Then there is the Port Authority Bus Terminal...
Things Not to do:
The TV musem is a HUGE let down, they have almost nothing for the $16 entrance fee. and more than likley they dont have anything to do with Jim Henson on display now.
MOMA - Might have something... I doubt it.
The Hot Dogs Stink in NYC - Stick with the Butterd roll or Knish

Use SPICY Brown Mustard