I think a lot of the convenience of the location of Union Station depends on (1) your tolerance for walking, (2) where you need to go, and (3) the weather. Washington is a pretty decent town for walking, with nice wide sidewalks in the downtown and motorists who (usually) obey the traffic laws. On my trip last week to see the doctor, I took the Red Line, a one-seat ride to Farragut Square and the K Street lobbyists corridor. I did have to walk a block to the doctor's office on Eye St. (The Red Line, by the way, also gives a one-seat ride from Union Station to the Zoo.)
After I finished with the doctor, I took the Blue line from Farragut West to L'Enfant Plaza and walked 2 blocks to the American Indian Museum. After I was done with my visit, I walked back to Union Station. It was a nice day, and a pleasant walk, all of the crossing of major streets had perfectly good traffic signals.
The Red Line to Blue/Orange/Silver at Metro Center to get to Smithsonian Station works perfectly well and lets you look at the intersecting barrel vaulted Metro Center Station. However, it's also not much of a walk down 12th St. to get to the Mall if you don't want to change trains.
It's also important to remember that the system was designed primarily to get people to and from work, and, as someone who used the Metro to get from Union Station to my office, it worked pretty well for that. I usually just walked two blocks down 13th St., but if the weather was bad (and I mean icy sidewalks or a real downpour), I could transfer trains and get off at Federal Triangle, right at my front door.