I always research unsafe areas for tourists when traveling to a new city, so when I run with my phone map I have a general idea of where I should avoid. Otherwise, I just turn down random streets, though populated and well lit ones. As to large crowds, I have only had this issue occasionally: just be ready to walk and don't be a nuisance to others. If it's a rural area, I mostly worry about surprise hills, not safety.

If it's a foreign country I am especially cautious as running is not really a hobby in many places. I wanted to go for a run by myself in Guatemala, but eventually decided that i wouldn't outside of very touristy areas or very rural areas. I had a great time running alone in downtown Montreal with minimal research. It depends on the country, so pay attention to local cultural norms and dress codes.