I used to live in Wheaton where my commute to WRAMC via car would take between 8 minutes (perfect conditions with lights still blinking yellow on Georgia, straight down Georgia to 16th) to 15 minutes (more common). Back home again could take 25 minutes or so. Going to NNMC was actually easier traffic-wise but took 20 minutes because I took back roads (PLyers Mills to Connecticut to Summit to Cedar).
Alternatively to WRAMC from Wheaton:
Via train - 10 minute walk to Wheaton station, 15 minute train to Silver Spring, 15 minute walk/bus to WRAMC (could go all the way to Takoma Park, too).
Via bus - 10 minute walk to Wheaton station, 35-40 minute (2 busses) to WRAMC.
Via bike - 30 minutes bike (back way past Forest Glen annex).
To NNMC from Wheaton:
Via car - 40 minutes MoCo bus from Wheaton Metro stop to Medical Center stop.
via bike - 35 minutes (same route as driving).
I wholeheartedly recommend the Wheaton/Kensington area, affordable (relatively), diverse, interesting, and as you can see pretty close to where you would need to go.