I guess it depends where you live, but I wouldn't be afraid of criminals. I've accidentally / naively walked through some of the more dangerous areas in the US for exercise and I've been okay. (I was visiting Philadelphia & thought I'd walk across the bridge into New Jersey to look around the city there, not knowing Camden is supposedly America's most dangerous city [1]... the people there were friendly to me but did say I looked lost).
I live in Australia and used to go jogging to a local lake and back (about 6km total), timing it so I'd get to the lake just around sunrise. There's usually a handful of other joggers there at that time too. Maybe see what other exercisers in your area do & where they go, if you're worried about being alone or targeted by criminals. Maybe ask a local running club.
Nowadays I have a membership to a gym down the street, and I go there at midnight (when the gym is usually empty). It fits with my current work routine a bit more than outdoor exercise does right now.
[1] http://www.dailymail.co.uk/news/article-2184246/Americas-dan...
