Actually the area around BCT was always a "tough neighborhood". Before the NYCRR started building the terminal the Buffalo Police had to evict many households with a bit of "extra strong persuasion". The railroad got the properties via eminent domain and the current owners where not too happy about it. But with some "rule of law" they were "moved along" out of the area of the terminal. The area around the terminal was never the "gilded" part of town.
The location of BCT was a bit of a compromise, the old (pre BCT) NYCRR station (near the south end of main street, or the "Foot of Main Street" to locals) had many operational problems. Through trains (NYC to Chicago) had to pull into the station and then back out to get back onto the old LSMS (or in NYCRR speak: "Lines West") route to Pa, Ohio... Chicago.
There where proposals to build a "Union Station" (about 1905) for Buffalo but those fell through. One of the proposals included loop tracks (like Grand Central Terminal) that would allow through trains to enter the station then depart around a loop that went back to the "mainline" west to Chicago. The NYCRR offered to rent space in BCT to the other passenger RRs in Buffalo (PRR, LV, TH&B, DL&W, etc.) before BCT was built but only the PRR and the TH&B were interested.
So the NYC went ahead and built BCT where it made the most operational sense for them hoping the additional economic activity around the terminal would cause the neighborhood to become more "Upscale". Sadly that did not turn out to be the case. In the case of Grand Central Terminal in Manhattan this is exactly what happened, covering over the old smoke filled railroad yards and selling "air rights" to build swanky hotels above the railroad generated enormous economic activity in mid town Manhattan. Remember that the tremendous economic growth in mid-town Manhattan north of Grand Central Terminal (completed in 1913) really took off in the mid 1920's. So it was reasonable to assume around that time that the same thing might happen in Buffalo, a fancy railroad terminal where all the connections to the outside world were concentrated and lots of inexpensive real estate that could become hotels and corporate headquarters, it made sense at the time. Perhaps without the Great Depression that part of town would have grown into something more "high end".
An interesting footnote, when they did the grading and drainage work for the terminal and the train platforms (including the underground baggage tunnel) they included future expansion for four more tracks south of the existing platforms (16 tracks if I remember correctly). They (the NYCRR) were very optimistic about the future of passenger trains and the demand for services. As I understand it all of the "prep work" to add four more passenger tracks (two additional platforms) was completed while BCT was built. Sadly those extra tracks where never needed. As Yogi Berri said: "It's hard to make predictions, especially about the future".....
I would check out BCT in the daytime with no worries, but I would not hang around much after dark, same as most inner city areas. I did arrive several times into BCT on the Amtrak Lake Shore Limited in the middle of the night back in the late 70's before they "shut her down" and never had any altercations, but that was a wee bit back in history....
Cheers, Kevin