Take a look at Google Maps for the various routes from the Udvar Hazy Center to your destination in Arlington. One of the choices is VA-267 East which is partially a toll-road. I haven't driven this way lately, but I think the toll is $1.75. I think the toll booth is manned, but to be on the safe side, I'd recommend having at least $2.00 in quarters with you if you drive this route.
Another route would be on Route 29 and I-66. This is not a toll road and would not take you too much longer than driving VA-267 since you would be driving against traffic in the afternoon.
It depends on where you are going in Arlington to drop off your car, but I would allow at least 45 - 1 hour minutes to get from the Udvar Hazy Museum to your final destination in Arlington on a Monday afternoon near rush hour.
Edited: 7:16 pm, April 14, 2013