I don't work for any of the hospitals in DC, but I have been transporting patients to many of the hospitals as a paramedic for a few years now. My information/observations come from that.
1. I know several nurses who drive an hour or more for their commute. Northern Maryland, eastern West Virginia, and Delaware are all places I know nurses commute from. If you're looking for immediate suburbs, I would suggest a place with reasonable metro access. Even though you're so geographically close, travel during higher traffic times can make it take 40 minutes to travel a mile up the road. Fairfax, Alexandria, Arlington, Rockville, and Silver Spring all have nice areas. Do your due diligence when checking out a new area.
2. I can't speak to much, but WHC has a published pay scale you can view from their contract. I've heard anecdotally that childrens pays less than others.
3. Medstar is the trauma service for Washington Hospital Center. WHC and GW are both very busy and have large patient loads per nurse at times. If you're interested in peds, there is Childrens National. Nurses I've spoken to seem happy there. Sibley is in north west and the ER seems nice. Other places with ERs that aren't as large are the VA, Georgetown, Howard University, and United Medical Center. Speaking solely as someone from the outside, I would never work at the latter 2 regardless of pay.