Adams Morgan , Columbia Heights are popular. U Street Corridor also. Vibrant. Son and his girlfriend live in Adams Morgan and that has been my favorite area to visit ( he also lived in Columbia Heights and Chinatown). He lived in Arlington initially after college but prefers DC( as do I). May be looking elsewhere in Adams Morgan or U Street Corridor soon. Prices are high in DC so prepare for that .
Yes people here do tend to fall all apart about winter weather. But frankly, most of them can’t drive in the snow and the rest of us are better off if they just stay home 
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I’m just reading this thread for the first time and wanted to mention that me D moved to DC right after graduation and lived there for 3 years before recently transferring to NYC. She loved DC and all 3 locations she lived in: Columbia Heights (OP mentioned it’s on the short list), Georgetown and Arlington. My D never felt unsafe in any of the areas she lived. Congratulations to your D and her husband on the new chapter in their lives. DC is great!
I’m glad they had a good visit. Yes, people do freak out whenever it snows, but that keeps winter interesting. DC rents are expensive, but you get more for your money than you do in New York or Boston. Both neighborhoods they are considering would be good choices.
I’m late to this thread. After she finished her Master’s degree D2 got a job in Rockville, MD. We went apartment hunting and I was impressed with Bethesda, but she had eyes only for DC proper. She eventually picked a place in Cleveland Park - a short walk from the metro station on the red line.
She loves DC and loves her neighborhood. She has always felt safe there. She has made a lot of friends and she loves to take advantage of all the many events, activities, restaurants, and general energy that DC has to offer. She’s a California girl, but she went to college in New Hampshire for four years, so the winter weather in DC is nothing that is going to scare her.
My wife would like her to move back to California some day, but I don’t think that’s going to happen in the foreseeable future. Daughter is having way too much fun.
My D attended college in DC, and I loved visiting her there. I really miss it. I know the locals hate the Metro, and it has a lot of issues, but compared to NYC’s subways, the trains and stations are so clean and modern and spacious. I found them a pleasure to use.
OP here with an update. They just signed for an apartment in Columbia Heights. They are very happy. It looks like each will have about a 35 minute commute. They will be able to have a dog in the near future and they are close to Rock Creek Park. And the unit has a washer/dryer in it-yay! The rent is just about what they were paying in NYC but this building is newer and they are on the second floor instead of being in a 4th floor walkup. I am happy as they are no longer above a restaurant- I worry too much about fires (and the restaurant brought cockroaches-ick).
Great! My sons lived on Kenyon Street for a couple of years in a rowhouse. It was a nice place to visit. Decent restaurants on 11th and 14th.