L.R.
It's extremely difficult to advise you until you know where you'll be living. You are willing to "drive her almost anywhere" but traffic in this region is very tough (the DC area is now one of the worst traffic areas in the United States, on a par in some surveys with LA and NY for commutes), so you may find you really do need to focus on the area near where you end up living. Driving from, say, Alexandria to Reston for preschool would be subjecting yourself and your child to a huge amount of time in the car, potentially, and isn't really necessary because there are so many preschools.
There are a lot of excellent preschools all over the area and any of the areas you mention have plenty of them. Are you visiting out here before you make the move in April? I would go online now, research preschools and then schedule visits for when you come out here. Check before you visit and ask whether the preschools are already booked up for this fall, or tend to have waiting lists; how long the waiting lists tend to be and how much of a real chance there is that a child who isn't at the very top would even get in; etc. I went to the information event at one preschool where they told us, only AFTER all the parents arrived, that they were fully booked for the following fall but we were welcome to go onto their waiting list -- that did not thrill me!
You also may find that "under $200 a month" may not get you all you would like for your child; I'm sure there are preschools that cheap out there but I would check their physical facilities and whether they offer extras like a music teacher or after-preschool programs where kids can stay on for an extra hour for special events etc. So be open to spending more. This is a pricey area and you may fall in love with a preschool that's more expensive than you mention.
