As Segovia, SirGecko and NavyCY have said its a matter of choice and Uncle Sam is very generous, so if you wish to live like a king you certainly can, (and if our military personal don't deserve too then who does?)
Here are the kinds of places one can get for $1600, very Frasier Crane like.
http://washingtondc.craigslist.org/mld/apa/1401970968.html
$1065 for a studio in a gated community with its own 24 hour convenience store, small but very nice. 5 minutes from USUHS by car.
http://washingtondc.craigslist.org/mld/apa/1404729209.html
$1100 full utilities, has own kitchen and bath, shared washer drier, (which is still better than laundramat) 1.5 miles from school.
http://washingtondc.craigslist.org/mld/apa/1398350754.html
$1200, 1 mile from School, apartment tower living with all utilities included. Fitness center and pool for those who believe in living well, underground parking site.
http://washingtondc.craigslist.org/mld/apa/1404262480.html
$1300 for 2 Bedroom, large with own washer dryer, 5 minute commute by car
http://washingtondc.craigslist.org/mld/apa/1400454183.html
$1425, luxury living with gorgous apartment in tower, washer dryer, pool the works, 5 minute commute by car.
http://washingtondc.craigslist.org/mld/apa/1402022233.html
$1550 luxury condo, 3.5 miles from USUHS, tower living with a 24 hour concierge, pool, onsite dry cleaning + washer dryer in every unit.
And for those willing to spend all the BAH on a place.
http://washingtondc.craigslist.org/nva/apa/1399354098.html
$1600 for a furnished luxury 2 bedroom in a gated community with 3 pools, underground parking, washer dryer in unit and all the bells and whistles.
Note, for $1600 you can also rent 3 bedroom townhomes, in case you have a big family, and if you have dependents you get $1900 BAH which can get you something huge, well equipped and on the doorstep of USUHS.
Personally, I have a passion for investing and hope to find something cheaper so I can put the extra $500/month into a long term small cap portfolio.
For those like me USAA has a fantastic career starter loan, $30K at 2% APR repaid over 5 years for $550/, month.
If you are frugal you can get this loan, incorporate it into your budget, get a nice place and still have $500/month to invest. Since time is on your side, having over $50K invested in your mid 20's means you can become a multimillionaire several times over (by your 50's or 60's), if you keep contributing to your portfolio as the years go on and you earn more.
Not that money is reason for going into mil med but to those that say mil docs give up great fortunes to do what they do, it isn't true. It all depends on personal choices and proper planning.
Oh and USAA is also great for auto insurance, a friend of mine in AF HPSP is paying $100/month which is $50/month savings.
Take away message: At USUHS your pay is generous and you are well taken care of, so focus on your job of studying and becoming a great military doctor.