We used Care.com to find our current nanny and were very satisfied with it. We had a specific second language in mind which made the searching easy for us because only a few nannies on the site met that requirement, and the second one we reached out to we immediately hit it off with.
Previously we were in a nanny share we found right here on DCUM (you can find those in the nanny forums, specific to whether you'll be in DC, MD, or VA -
https://www.dcurbanmom.com/nanny-forum/forums/list.page). That was also a good situation with a wonderful nanny and other family; we only left because we decided it was time for DC to begin picking up that second language.
And yes, at $20 you should be able to find an excellent nanny around here, especially assuming you have just one child. Good luck!