I used to live in Dayton and yep, I can think of several places where the bike paths go through not-so-wonderful neighborhoods. You might check the map for possible alternate routes; going a mile out of the way will only add about 5 minutes to your ride and would take you into a much safer neighborhood. (For example, cutting through Kettering and Oakwood on neighborhood streets instead of going up the river after dark.) If you don't feel safe in a specific area, then you probably need to find another route. Also, an area that feels unsafe a night might be perfectly OK during the day. At what time of day do you need to make your commute?

As a cyclist on the bike path, you will have an advantage in that you are moving quickly and quietly without many stops. My experience as a bike commuter is that crazy people and panhandlers both are far less likely to approach me than they are when I am on foot. I suspect that they assume that I don't have any money. When I had to drive through unsafe areas, I worried much more about being carjacked than I do now about having my bike stolen out from under me (riding a bike with dropped bars and clipless pedals helps with that - many people simply aren't going to be able to ride away on my bike). My biggest worry usually is drunk/high/bored teenagers and drunk drivers; I tend to stay off the road on weekend nights.

Something I really miss about Ohio is that everyone I met on the trail in the morning always said "Good morning" or "Hello." It was such a nice, cheerful environment.