Oswego has few major crimes. In the last six years there have a total of 1 murder, 10 rapes, 90 robberies according to the crime records. Burglaries and Thefts (shop-lifting, garage and car break-ins) have been the most prevelant crime and those are not ones that effect tourists who use common sense precautions.
Lock car doors; put valuables in Motel safe and use a money belt so you aren't flashing large amounts of cash. Use ATM machines in well-lit, crowded places during normal hours.
Know who is near you and keep an eye on the kids. All these actions should help to not be a target and will help insure that you have a pleasant, safe time in Oswego.
Ask your hotel staff if there are any parts of the city to avoid at night. They are locals and normally can guide you away from potential dangers.
There are 35 sex offenders in the greater Oswego city area. This is not an inordinant amount of SOs for the large population of Oswego but if you are concerned then check out the website below.