The next core-collapse supernova in our Galaxy will be a spectacular event, with some $10^4$ neutrino detections in total expected among several detectors. This data will allow unprecedented tests of neutrino properties and new opportunities in astrophysics. In this paper, I focus on two main topics: (1) Measurement of the $ u_mu$ and $ u_tau$ masses by time-of-flight, with an emphasis on introducing as little supernova model dependence as possible, and (2) Methods for locating a supernova by its neutrinos in advance of the light, which may allow improved astronomical observations. In the latter, I also discuss the recent result that the positrons from $bar{ u}_e + p to e^+ + n$ are not isotropically emitted, as commonly thought.
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