You can find out about pretty much everything in most towns/cities by logging onto the following webiste:
and filling in the location you're looking for, eg. Beacon, NY, in the search area. I know Newburg, Poughkeepsie and Middletown have a very high crime rate. Am not sure about Beacon.
Check it out for yourself. It's very helpful and informative.
It is hard to say without knowing what specific map you are looking at.
I am a real estate broker who lives and works in Beacon.
I have lived here for 8 years and have no complaints at all.
Of course, there is crime here just like everywhere else in the US.
I know it can be hard if you are relocating to a new area.
Feel free to let me know if you have any questions.
Thanks and good luck with the move!
Licensed Real Estate Broker
Anna has it correct, you should contact the local police departments to determine if Beacon is an area you may or may not want to live. Here are some phone numbers:
City of Beacon Police Department (845) 831-4111
Dutchess County Sherrifs Department (845) 486-3800
Hope that helps!