Is the Chicago Greyhound station on Harrison safe?

It's not the safest area, but it is near an upscale neighborhood near the U of IL Chicago campus. The area is pretty close to the gentrifying West Loop neighborhood.

Just stay on the main streets, and don't look bewildered or lost. And IGNORE panhandlers.

PS: Did you know that Amtrak runs a lot of trains between Milwaukee and Chicago?

yes. They have security guards on site and they try to keep the riff raff out. However, once off greyhound property, you'll have all the seedy people, gypsy taxis, drug dealers and such. If you need to go somewhere, walk with purpose. Know where you're going (use google maps on your phone)