The Real Estate forum will be able to provide more information for where to live:
https://www.dcurbanmom.com/jforum/forums/show/50.page
In your post, I'd clarify your needs: budget, townhouse/house/apt, how many bedrooms/bathrooms, etc.
You say your wife will need to be in office, but we don't know where her office is.

We also don't know what a reasonable commute is for her. Under 30 minutes? Under an hour? Car vs metro?
Nanny wise: what does full time mean to you? What hours are you looking for? Will you need more than 40 hours per week? If so, you'll need to factor in overtime pay. I'm going off the assumption that you plan on paying taxes and doing things legally.
Will the nanny need to drive to pick up the older child? If so, plan on paying the IRS rate for reimbursement for mileage.
How many hours daily will the nanny be watching both children? Keep in mind other days -- snow days, holidays, teacher work days, summer break, etc. If she'll be responsible for both, take that into consideration for pay.