Prospect St. is fine. Once you start heading toward Winchester, it gets dicey. Would avoid Winchester from Division St. to Goodrich / Morse.

Eta: although Newhallville is considered high crime, most violent crime isn’t directed at random people. Keep alert and aware and mind your business and you’ll be ok in most areas of the city. Property crime is common throughout New Haven, including the neighborhoods considered “safe”. The city regularly shares “Compstat” reports about crime, they’re a bit difficult to read if you’re not familiar with the area. But it’s a good source for major crime data. Click on the time period you’re interested in viewing, then Scroll down to “District 7”.

https://www.newhavenct.gov/government/departments-divisions/new-haven-police-department/compstat-reports/-folder-77

Edit #2: according to above link, during last 2 weeks, gunfire was heard corner on Highland and Winchester, and larceny from vehicle was reported on Sheffield and Mansfield. This district also includes East Rock, which had its own issues with property crime last week.