Hi, OP. Your best bet might be to start with this site:
http://www.dss.virginia.gov/facility/search/cc.cgi All providers registered by the state are tracked here. It allows you to search by in-home versus center and by zip code. Best yet is that you can also see their background of inspections, types of violations and so on. Arlington County also has a list of licensed providers but it doesn't have this level of detail.
Now is a good time to be talking and interviewing, spots often open in September when older kids head to preschool or kindergarten. Despite what a PP said, there are a fair number of providers, it's the availability that's a challenge.
Daycare costs run the gamut. We pay $230/wk, which includes 2 meals plus a snack. Our provider is open from 7:30-6pm M-F. All those types of things vary by provider.
good luck!