It ain't DC...but it's a good break from Washington's crime, traffic, and tourists, tourists, TOURISTS!
First, the best way to get to Alexandria is the metro, the greater Washington area's commuter rail. Take it to King Street, which will drop you right in Old Town.
The first thing you'll see at the metro station is a HUGE, strange, phallic-looking, temple-like thing behind you on a hill. It's the George Washington Masonic Memorial - remember, this is GW's home turf, and that monument was built by the same Mason's lodge he belonged to. It's open to the public and worth a visit because 1. It holds a good deal of GW memorabilia, and 2. The guide will take you to the top from where you can see for miles, and miles, and miles...
After visiting the Memorial, walk east on King Street - King will take you straight to the Potomac River. As you walk, you'll see a lot of shops and restaurants...quick recommendations: for TexMex, Austin Grill can't be beat. For Indian, check out the Taj Mahall. For Italian, Tratoria di Franco, which is one block South on Washington Street, which intersects King. And further down King is Gadsby's Tavern where someone famous once ate - you guessed it, George Washington.
And that intersection, in fact, is where things get interesting. Walk one block right on Washington, and you'll see a large statue of a Confederate soldier in the middle of the street. It's dedicated to the town's Civil War dead, and, amazingly, people still leave flowers at its feet. The building right near it, the Lyceum, which looks (kind of) like a Greek Temple is actually a visitor's bureau, a good place to pick up a map and ask what's happening in town. If you walk for another block or two, you'll see an old school that GW endowed for the children of orphans; later, it was converted to educate African-Americans.
Now back to King and Washington. If you turn LEFT (North) at the intersection and walk for a block, you'll come upon ChristChurch. This is where GW himself worshiped, and if you're like me and like to haunt old cemeteries, its small but beautiful grounds make a nice two-minute stroll. Check out the group grave of Confederate war dead, too - again, this ain't D.C. Walk for another block or so, and you'll see the Lee Houses. Yup, named for and occupied by THE Lees, of Light Horse Harry and Robert E. fame. Worth a visit...and check out the nearby cobblestone street, too - preserved from Alexandria's past, and supposedly paved by Hessian POWs during the American Revolution.
And back to King and Washington once more. If you stay on King, you'll get into the heart of Old Town. Small shops line King Street - offbeat art, antiques, a couple restaurants, and so on. For a good beer, try Founders (though the service is terrible) or Pat Troy's, a friendly Irish bar run by, of course, Pat Troy, who has lived in Alexandria since George Washington's day.
Right near PT's is town square. During the summer weekdays, musical entertainment and fountains are going, and it's a great place for sandwiches and people-watching. Plus, plans are in the work to make all of Old Town a wireless hot spot over the next few years, so, as you're enjoying your lunch, you'll be able to write me to thank me for this helpful advice. No, my pleasure.
As you're walking in this area, enjoy the old architecture (and gawk at the outrageous property values...LOTS of old money here), and wander about a bit. Many homes with cool signs: "Lafayette slept here"; "The original ice house" (which was used to keep the dead from rotting, pre-burial, as well...); and my favorite, my being a transplanted Yankee, "HQ of the restored union government of Virginia."
Push on to the waterfront. On nice nights, local entertainers come out here. Some suck and are a waste of time, especially the guy who can play two songs on a recorder. Others, though, are fun - classical music, performance artists, doo-wop groups. For the kiddies (or kid-like adults like me), visit the folks from the Parrot Rescue. For a small donation, they'll snap your photo with 15 parrots standing on you. You provide the $$, they'll provide the parrots.
And you've hit the Potomac...what now? Well, you can catch a DASH bus back to the metro - they run up and down King Street regularly, for only a buck. Or, if you have the time and money, you can hop a boat back to D.C. In the evenings and on the weekend, regular "shuttles" run up and down the Potomac from Alexandria to Georgetown. Or, if you want to stay in Alexandria, why not book a dinner cruise? Very romantic - try Nina's Dandy or the Dandy for a fair deal. (HINT: visit the couple tourist booths around town, and they'll give you a map which MAY have a cruise coupon in it.)
Last: What about the kids? Well, we've done the parrot people...how about a ghost tour? They leave from right near town square (the Athenium, the building is called). Or, if you're looking for kiddie food, drive (too far to walk) west on Duke Street for a few miles to Generous George's Positive Pizza Place. It's the poor man's Chuck E Cheese's. You lose the games, but get twice the bad food, and triple the gaudiness. (If you want the real Chuck E's, head south on Route 1 for about 3 miles...)
There you have it - maybe "The Fun Side Of The Potomac," as the DASH buses advertise, is an exaggeration, but quaint and a good day trip, nonetheless - Alexandria, Virginia!