Do you think Alexandria might feel uptight compared to Anacostia and Benning Road? The author is partly expressing a comparative judgment - that's kind of the point, going for a walk in a much poorer black neighborhood vs strolling past the perimeter of Old Town Alexandria.
One expression of what I might call "uptightness" that you might hear from DC area residents is an overt fear of even driving through certain DC neighborhoods (or maybe even Southeast as a whole!), as if they were active war zones and not just a place where the signs of low social maintenance and low-income lives of black people are unmistakably visible. It makes sense, the crime stats are worse; most people have no reason to visit these neighborhoods and see what they're like; everyone has heard stories about how bad DC was decades ago and these neighborhoods hold the bad reputation.
In my opinion, people being "uptight" in this way is a mix of "common sense" (maybe it doesn't reflect reality, but if people act like it does they really pay no price) and "hysteria" (other people told me I ought to be extremely afraid, so I will be). [scare quotes added to emphasize that these are my subjective judgments and, imo, inescapably subjective.]