Begin your quest at the National Museum. Aside from the usual items you need to get special items that will get you further in the game. For the Geocache, you'll be needing to look for John Hancock's Fountain Pen. You'll find it in the bookcase to your left; it's red and looks like a pencil. Another item to look for is a safety pin - you'll need to use the Brush (part of your tools) to get it. Brush the edge of it and use the right bookcase. Now to find the Brooklyn Map, you'll need to gather 5 red books scattered around the National Museum. Arrange them all on the table and then use the paper you find and rub the charcoal over it to get the map.
Moving on, you need to go to the Empire State Building where again you'll need the Geocache item. This time you're looking for the State Building Foreman's Hard Hat (you'll find it under the left glass display case). Now to get the Number 8, you'll need to use the brush again above the right corner of the desk. The UFO will need to be dusted too - it's to the left of the bottom of the Empire State Building. The CIA will be attained by breaking the white square with the hammer on the lower left. To get the Allen Key, you need to break the flower pot on the information desk. Now, you need the Allen Key to set the clock to 6:12 revealing a secret compartment.
Once you're done here, pack up and head to the Retired Federal Reserve where the Geocache item is a 1798 English Dueling Pistol found inside the safe door. To get to the Blueprint, you'll need to get the Key from Grant's Home. Use the it on the safety deposit box inside the safe. Get to Grant's Home and get General Custer's Coat Button (left edge of the light fixture) for the Geocache. The money can be found by breaking the mirror as opposed to breaking the flower pot, which will get you the shotgun shell. A key - the Golden one - will be found on the mirror on the left side, whereas the Key that you need can be found by using the key you used previously to open the clock door. You need to hang three weights and click on the Painting in the upper right. Move the weights around to match the picture.
Now its time to get to the New York City Docks, where the Geocache item can be found on the boat railing (its the USS Princeton Steamship Propellor). Get the Pears and the Oil can on the crates before you leave for the Brooklyn Bridge. (To leave, you need to cut the ropes and use the keys on the boat)
Finally, at the Brooklyn Bridge collect all pertinent items as well as John Roebling's Pocket Watch for the Geocache. Dust the bush and the bridge base to collect the tennis ball and the 1804 sign. Now use the crank handle on the winch and lower the scaffolding to find the water on the right. Use the Destiny Scanner on the lower center of the bridge base, use the pickaxe to reveal a door, and open it.