Chevy Chase would be a very nice area or even Bethesda. But can be pricey.
My wife is Navy and works at the Bethesda Naval Hospital which is right across Rockville Pike from NIH. We chose to live in Kensington and she has only a 4 mile commute to work. It's a very laid back community and found it to be very safe and family oriented. You can find a house to rent in the range of $ 1600 to $2500 for a decent house. There were other parts of Kensington that were only 1 or 2 miles from the Hospital , but we liked this house and found it still to be an easy commute.
There are plenty of ammentities around and depending on exactly where you live metro is not far away if that's still needed for yourself after you find work.
Just remember one thing here in the DC area is TRAFFIC. My wife leaves early for work so there is little or no traffic for her at all. But if you leave around 7:15 or later that same 4 miles can turn into a 20 to 25 minute drive at times. Traffic is very crazy here !!! Good luck on your search.
