Welcome to the area! Here are a couple of ideas:
The Fairfax Co library system does tons of free or almost free activities in the libraries. Trips to the library are also great - picking out books and sitting down to read them in a comfy chair. Go here to look up library events: http://www.fairfaxcounty.gov/library/programsevents.htm (you can search by branch or by type of activity) Many are free or very minimal cost and it doesn't matter if you're a Fairfax resident, you just have to be willing to drive to the library branch.
You should sign up for the Park Service's e-newsletter that tells you about all of the activities at parks and rec centers. There are a LOT of parks with great playground equipment! Here's the calendar, you'll need to find the spot to sign up http://www.fairfaxcounty.gov/parks/calframe.htm Some of these do have fees, but they are very reasonable. Also, you should sign up for the Parktakes rec center class catalogue (published 2 times a year) to see even more options.
Out in Herndon is Frying Pan Park (free admission)- great to go to for an hour or so outing - its a farm park and all the new baby animals start being born in February! They also have special events (for a minimal cost) throughout the year (Milking Day, Sheep Shearing Day, etc.)
Another neat/short outing is your local pet store - they make great mini "zoo" trips. Some furry, some scaly and just the right amount of animals to keep a little one's attention. All indoors, which is great in the winter - head to the National Zoo in the spring!
Your kids are a little young to get much out of the rest of the museums and monuments, but it's worth toting them along so that YOU can see them and get out and about when the weather is nice.
There are also a whole bunch of Mom's groups all over the place - through churches and hobbies/interests and locations. This is a wonderful area to live in - if you can deal with the traffic and politicians. = ) Enjoy!
