This is a common question asked by folks that are considering moving to an area. Real estate agents are instructed to avoid answering. The concern is that any negative feedback could be construed as "steering" which is an illegal practice. It is within guidelines to direct consumers to websites that feature crime statistics, etc.. This method removes the agent from offering an opinion. It also overlooks the basic fact that steering involves the use of race as a determining factor.
In my opinion, criminals commit crimes and criminals come in all colors. Statistics are valid if you are determining the amount of police officers committed to any one area. They really don't help much if you are a student attempting to determine the safety of any neighborhood at various times of the day and night.
I have lived and worked in the DC area all of my life. Neighborhoods are constantly in transition. The relative safety of one area over another usually is found in the individual perspective of each person. What one considers "safe" another may consider "unsafe".
How do you decide? My suggestion would be to meet with someone you know and trust and visit the area around L St NW in several different times of the day. Walk from Mt. Vernon to L St and back again. Pay attention to your surroundings. Try and get a sense of how you feel. Make sure you take the trip at least two or three times in one week. If folks are sitting out, stop and say hello and ask them how they feel about the neighborhood.
In the end, you have to believe what you see and hear. There is nothing I can share that will give you the same sense of relief that you will find after personal visits.
While in the area, check out the coffee shops and the locations (if any) of the bike share racks that are located throughout the city. Walking is optional. I know this is not a perfect answer, but I think a little time spent on your part will help you find that comfort zone and you will have the opportunity to know and love DC.