The Southside Hill is taxed no more than anywhere else in the City of Corning such as Houghton Plot or the North Side.
The taxes are an old, layered system consisting for the most part of
#1 town/county tax
#2 school district
#3, city or village tax, if one applies.
As a result, the Town of Corning will be cheaper than the City due to the lack of the city tax, but the city will all be taxed at the same rate. The Village of Painted Post is high due to the extreme Village tax there, but the rest of Painted Post (which is actually the town of Erwin) is very reasonable.
As a result of this system, you cannot assume that the taxes are going to be high because of a home being listed in Corning or Painted Post. The exact municipality, not the mailing address will determine the tax rate.
Corning's (city) property values are based on the strength of the school district and Corning Inc. stock. Southside Hill is clearly the best neighborhood for holding / increasing housing value and is subsequently taxed the highest. Painted Post also holds value well but is taxed even higher with the appropriate return on municipal services though. In my humble opinion, there is not much holding Elmira together...
My wife and I are looking in Corning, preferably Southside Hill within walking distance to Market Street, or out in the country in a decent neighborhood / region with some land to spread out. Good luck with your search!
Ms. Brocco is right, check with the local police departments and if any locals are on Trulia, I am sure they will weigh in. I think you will find most agents reticent to comment on these types of things and will direct you to third party sources due to legal reasons. I own a home in the Finger Lakes region, and find the area to be lovely, however, it is a vacation home and about an hour from Corning, so I cannot comment intelligently on the crime issues. We don't even lock our doors at night!
Best wishes, Jim