We had decent luck finding street parking in the area in the past. If you can avoid a rental car, do so, but if not you could probably find overnight parking for it. IIRC, I had to go north and west a bit and walk back a few blocks. For a nondescript Grand Am or whatever I had, I didn't worry about it being parked outside. Nobody messed with it.

Definitely second the recommendation for the "old wing" - nicer and more convenient to get out to the street as well.

Woodley Park is one of my favorite DC neighborhoods. ^

The only potential issue you could run into at this hotel is a large convention. It has one of the biggest ballrooms in DC, so if there's an event there chances are good it's a BIG one with all of the resulting obnoxiousness and inebriation that goes along with it. However, since you're seeing a lot of attractive rates for this weekend, that leads me to believe that the hotel isn't booked solid with one of these events.