This may not be what you're looking for, you can take the kids but it's definitely a fine dining establishment. Some people might find it

We didn't and we're your average blue collar folks.
http://www.1789restaurant.com/main/index.shtml
I recommend them because we went to DC for our 6th wedding anniversary 2 years ago. I was dying to go there but they were booked solid. We were celebrating not only our anniversary, but my 5 year survival of a rare cancer my Dr had said had a 100% mortality rate within 5 years. This was a VERY special occasion to us. I had asked to be put on the waiting list in case of cancellation and the lovely lady I spoke with was quite chatty so I wound up giving TMI about us. She promised to do everything in her power to get us in. This with less than a week notice.
On a whim, I called her from a museum to see if there'd been an an opening. She asked if this was Mrs. Drawers and when I said it was she said she'd been trying to call my cell all day, that she'd MADE an opening and could we be there in 3 hours?


She asked where we were staying and said someone would call for us at 7pm.

Imagine our surpise when a LIMO driver came to pick us up and took us to dinner! They called us by name (I'm sure they let each other know who we were since we'd never met), treated us like royalty, gave us a bottle of their best champagne with their best wishes and priinted a copy of the menu with our names on the bottom and the date. Service was excellent, food was great, and for all we got the price was surprisingly reasonable. We never felt out of place even though we recognized a couple WA DC big wigs in the room.
As it turns out, the mother of the woman I spoke with died from the same cancer I had and she said her mom would want her to do something nice like that. Her mom would be proud. I sent a heart felt thank you note and this photo of us at the B&B taken by the limo driver as we were leaving for dinner.
We go there every time we get to DC. It's worth every single cent.