When I visited DC back in 2011 my brother and I didn't make it to the National Postal Museum there was so many things to see and do.
Anyway, I see that the collection is online for viewing. I've spent about 30 minutes exploring the different areas.
I know it isn't the same as seeing it in person but for me, I think it's interesting.
Here's the link
http://arago.si.edu/flash/?tid=2027477|s1=1 There's a drop down arrow next to the world Philately that is how you navigate.
Enjoy.