I was raised in the D.C. Metro Area.
Actually, I've lived around there a couple of times. First in 1979 I lived in Vienna, then I actually lived in Washington D.C. in Woodley Park, and then back in Vienna again while I was in high school.
I LOVE the DC Metro Area... honestly... there's just nothing like it. As Bob Hope says... "I love D.C. that's where my money is..." (or something like that)
There's soo much to see, you really can't do all of D.C. in a weekend, but if you plan to spend a week there, it's worth it!!!
If I'm honest, you probably don't really want to bring your Fiero there as you won't actually be driving it at all. The Metro will let you go anywhere you want to go short of a few places like the 2nd Air & Space Museum which is off Dulles Road. Speaking of... even the Dulles International Airport is worth cruising by. It's amazing architecture. It was designed by a famous architect which designed 60s mod furniture (among other things). It was named after the guy who started the intelligence agencies.
There's SOOO much to see and do there. I've lived in South Florida for 15 years now... and even though I feel like I fit in so well with all my Hispanic peeps down here, Washington D.C. is my home...
I guess this is what I would do. Drive up there, and stay at the Wolf Trap Hotel in Vienna Virginia (it's very cheap, and only 1 mile from the subway). But if you want slightly more convenienve, and don't mind spending a lot, then you can actually get a hotel in D.C.... although understand it will be probably twice as much.
End up at the Metro Center (some of the longest escalators in the world, it's worth it just to see that...)
Head to the Smithsonian. On your FIRST day, I would suggest picking a side of the Smithsonian and walk up and down it visiting the various museums. If you have time, you can PROBABLY see the other side too. They have the Natural History Museum, Air & Space Museum, and then there's a few others. I've never been able to make it into the Holocaust museum or the Native American museum becuase every time I'm there, there's a line going out the door.
You will spend the entire day doing that.
The next day, I would make the track from the Smithsonian all the way to Arlington Park Cemetary. It's a long walk, so hopefully you're not old as dirt...
This will take you across the WW2 memorial, the Washington Monument, the Vietnam Memorial, the WW1 memorial, and all the other memorials along that way, including the Lincoln Memorial. If you go off to the side a bit, you can see the Jefferson Memorial, as well as the FDR Park, and some others. There's actually quite a few smaller memorials that are hidden away in the forest, some of which are actually in various states of disrepair that you don't even know what they're for.
Anyway, then you make your way across the Arlington Memorial Bridge, which in itself is also a monument. Parts of it were donated by Italy, and other parts from another country. After you cross the way, you'll cross the street and make your way to the run that heads down to Arlington Memorial Cemetary. There are a number of memorials up and down the sides from various smaller wars, or lesser known wars I suppose, like the Spanish American War (had a GGG grandfather in that), plus some specific units in the Civil War have some memorials there. Once you enter the Cemetary (I think it closes at like 3:30 or something early, so plan ahead), there's a lot to see there also. Remember of course it's a cemetery, and like with the other war memorials like the Vietnam memorial, WW2 memorial, etc... you're supposed to be very quiet. It's not uncommon to get choked up, and I usually see half the people there crying... it's the sign of a true American.
Once you're done, there's a Subway stop right at the bottom of the hill (entrance at the memorial) and you can just take that right back to your hotel, etc.
The next day, you might want to see if you can make an appointment for the Treasury / Mint... just to see if you can get a tour. There's also as I said, the other Air & Space Museum off the Dulles Toll Road.
You'll also want to check out the White House, the Capitol, and of course, the House of Representatives building where you can go and see your rep...
There's some famous places where you can go eat, or have a beer. I forget the name, but right across from Pennsylvania Avenue, there's a bar where most of the congressmen go to get a drink. I would go there from time to time when I visit, and there's always someone there (if you know your politicians).
Anyway, it's a blast... it really is... I highly recommend you make the trip there, as I know you'll enjoy it as much as I and everyone else has. It's all free too... after all, you already paid for it.