Hi! Maura had a ton of great suggestions, but I wanted to mention a couple of corrections:
The Spy Museum is definitely not for young children - they don't recommend it for kids younger than 8, so if you want to go, go while your son is an oblivious infant. It gets great reviews, so it is worth the visit, but go before your son is paying attention.
I went to see Ford's Theater last summer with my sister while she was in town - turns out that it is closed for renovations for a couple of years. I think it is supposed to re-open in late 2009 or in early 2010, so push that one later in your calendar. = )
I have some additional suggestions for you:
-the Cherry Blossom parade and festival in late March/early April - great photo ops and the parade is nice, without being exceptionally crowded. If you don't make the parade, at least get down to the memorials and take some pics up against all those blooms. = )
-The National Zoo is great (and free!) If you can, join the Friends Of National Zoo (FONZ) - they have tons of special events geared towards little ones, some are invitation only to FONZ members while some of the tickets go on sale first to FONZ members (and they sell out fast)
-visit Mt Vernon - the new educational center is awesome and plenty to do if the weather is not so great, but try to pick a sunny day to toodle around the grounds and main house as well. Best times for this are spring and fall when the temps are not too extreme. (This one is not free.)
-take one of the boat tours from the Old Town Alexandria dock - you can go up to Georgetown, disembark, stroll around and then get back on a boat for the return trip, or they have a boat that goes down to Mt Vernon for the day and then sails back to Old Town in the evening.
-when your son is a little older - Baltimore's Inner Harbor has a great Children's Science Museum, a fabulous Aquarium and is a great place to walk around on a nice day. They are pricy though, so go once he is old enough to appreciate everything.
-The brand new National Children's Museum is scheduled to open in the city in 2009, so keep an eye open for that.
-If you are into/interested in handwork, there is a Textile Museum, a Bead Museum, and a Smithsonian devoted to arts and crafts.
-For interesting walk-abouts when the weather is nice, check out one of the semi-local plantations (Sotterly in Hollywood, MD and Sully in Chantilly, VA), or the archeological digs in Old Town Alexandria or of the colonial settlement in St Mary's County, MD.
-In the summer, a great day-trip is out to Bealeton, VA to see the Flying Circus Air Show (with biplanes and wing walkers, oh my!) they also have a hot air balloon festival every year too.
-Some great museums I have to mention:
National Museum of Women in the Arts (LOVE it!)
National Geographic Museum at Explorers Hall (Fabulous and free!)
National Building Museum (check the special exhibit)
(and more at www.culturaltourismdc.org)
-Finally, we have a great show/concert/arts venue here in Fairfax - the Patriot Center on the campus of GMU. My daughter's preschool class is going to see an Elmo show there on Dec 12th, so keep any eye on listings for that to see if anything coming through is something you or your kiddo might like as he gets older. They have something Sesame Street every fall and some kind of Disney on Ice every spring, and the RBB&B circus every year too. There are concerts etc for grownups all year long too. Worth keeping an eye on! www.patriotcenter.com
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One word of caution - don't bother with the "National Aquarium" in downtown DC - checked it out last summer with my sister and her kids and it is definitely not worth the money or the wait - half the tanks were empty!
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Have fun exploring and let us know if you find anything else good - I've lived here for 15 years and I still haven't found everything! = )