A good playlist and somewhere interesting to explore make it great, but I also just love running. I bring running shoes when I travel: there's nothing like running through a new city as a tourist.
That last bit gives me a ton of anxiety just thinking about it. Do you map out where you can run before you go to a new place? How do you just like run on the sidewalk if it ends up congested with too many people? Do you only run in nearby parks?
Sorry if these are weird questions! I legitimately want to know!
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.