Keene is a wonderful city full of great people. Cost of living in the city is high though and tenants have come to expect it. I calculate taxes, vacancy and property management (currently self managing) into my figures and entertain the properties where the numbers cashflow. It is possible to do well in the city on the right properties.
I don't believe there are any truly terrible neighborhoods to stay away from. The college brings in a 3000 new faces every year. Main street is usually a very happening place. We do have our share of crime but it isn't anything that keeps me up at night. I suppose the only drawback that I can think of is that all the buildings here seem to be built circa year 1900. Be sure to factor for upkeep in regards to this and have a good building inspector go through before the purchase. (references available if needed). Keene is also founded on low-lying wetland. In the last two decades we did see two significant floods which caused a lot of damage to a lot of property. Flood insurance is a must in some areas and can be expensive. (also have references for this if needed).
All-in-all, I love it here and believe buying my MF is one of the best things I have ever done. I am also interested in adding more units whenever this market cools down. Overall, Keene is a great place to call "home".