What is your formal pick for DC?
Ok, out of these restaurants, which are elegant and formal restaurants for teenagers?
Taberna del Alabardero
Yabba Pot (Virgin Islands/Caribbean-influenced vegetarian/vegan - not gonna find that in too many places!)
Ras Doobie (good Jamaican, and Doobie is just a really wonderful, gentle soul)
Martick's (quirky "French influenced" in the most anonymous location imaginable)
Matthew's (unique style of pizza)
Joe Squared (unique style of pizza - sourdough crust!)
Let me know!
With or without parents? Two 14-year-olds or 20 seniors before a high school prom?
Some of those are neither formal nor elegant by anyone's standards.
My guess is you are looking for something that is not super expensive or formal, but still is elegant. I have two recommendations: Restaurant Eve (in Old Town Alexandria, not in DC) for quiet, classic. Zaytinya for chic, bustling. No reservations after 6:30pm at Zaytinya, so you might have to wait for a table if you plan on eating later than that.
Out of these restaurants (or those of your own), which of these could I take my girlfriend, plus her 11 year old and 14 year old to impress them? Any suggestions?
Mansion on O, because it's like a playhouse.
701 because it is hushed and plush, has a piano, and has a wide menu that even includes mini-burgers.
Dino, because it has lovely service and an accessible menu.
All three will make 11 and 14 year olds feel very grown up and still have foods that they will easily recognize and enjoy in very pretty settings.
From the list you provided, I'm inclined to select the Palm if the kids like steak or lobster, because the kids will be entertained by all the caricatures on the wall and might have a pretty good chance of seeing a real live celebrity, too. Plus, the steak and lobster are as good as you'll find anywhere.
The Palm has an unfortunate tendency to fawn over its regulars who spend $1000s each month on fat expense accounts. Watching the staff lavish attention on celebrities won't make up for being ignored if the kids aren't treated as special guests too.
There are other places with great food that may treat them better.