Without knowing too many specifics (like your perception of quiet time and nightlife), I'll get the ball rolling and take a stab. I'm starting off with the assumption, based on your location info below the post, you are talking about a two hour drive, not flight and $300 for two nights hotels, each of which of the following I've stayed at and found to be fine service:
Bethesda Md. - Residence Inn Wisconsin Ave. - you can often get rates below $150 (even less with AAA) on weekends. Avoid parking charges by parking in the Montgomery County lot around the corner which is free on weekends. Restaurants, theatre (Round House 100 yards away), night club (Bethesda Blues and Night Club), movie theatres, and lounges all within walking distance.
Alexandria Va - Spring Hill on Eisenhower Ave. - Free parking - same as above, plenty to do (Little Theatre of Alexandria, restaurants, clubs etc) Masonic Temple is a nice (free) visit during the day with a great view of DC and surrounding area.
Philadelphia - Airport Renaissance - quiet during the day (has a nice bird sanctuary) and can drive (free parking at hotel) into city for nightlife
Charlottesville - Fairfield Inn (non football weekends) - can hit local wineries during day and college town, here's where definition of nightlife comes into play
Richmond - Residence Inn - Dickens Rd. (Downtown Marriott exceeds budget plus parking fee) - easy drive into downtown with clubs, restaurants, theatre and concerts etc; quiet during the day to your level of interest
others to look at;
Baltimore - Camden Yards Marriott (but with parking goes a few above target) Inner Harbor with all of its offerings
Annapolis - because the property is small, you seldom see the Marriott below $250 per night, but the nearby SpringHill works just fine (free parking) excellent restaurants, the Naval Academy, water, and the Rams Head Tavern has some entertaining shows
Dulles Va - Dulles Marriott Suites - great rates, free parking, nice pools, in a shopping area, yet quiet, Udvar Hazy Museum (Smithsonian Air and Space) is just down the road and you can go into Reston Town Center for activities at night (Next Stop Theatre is nearby with cabarets and shows)
That might get the conversation started. Good luck wherever you end up.
If you prefer a quiet evening, with excellent food in small, picturesque setting, within two hour drive of Washington, DC, try the Bavarian Inn: Bavarian Inn WV
You can stay in the Inn, or in a lovely cottage overlooking the Potomac River.