The great thing about running is that you can do it anywhere. You don't need any special equipment except for good shoes and a sports bra with good support (women only for that second item). When going on vacation, you don't have to schlep a lot of equipment or look for a gym. You just put on your running clothes and go out the door.
I almost always brought running clothes when I went on vacation and have run in some interesting places. On a trip to Portugal I found a cross-country trail near my hotel. As I was running, it seemed like everyone else on that trail was zooming by me. Everyone was passing me like I was standing still. Afterward I found out that this trail was used for training by elite runners. There was one group of elite runners from Germany at my hotel. I saw other people walking around with t-shirts from high-level competitions. I didn't feel so bad about being passed after that. When I took trips to Bibione, Italy the running gear came with me. I liked running on the path along the beach before the weather got too hot and the crowds came out to the beach. I've also run in the Austrian Alps.
When I go to the States to visit family and friends, I always pack the running gear. I have run in Boston, San Diego, Los Angeles, Lone Pine (CA), and Novato (CA) while visiting. I had a strange experience in Novato, where I was visiting my cousin. I ran to a park, where there were some nice-looking trails. As I was running on a trail, there was a group of 4 people (2 men, 2 women) in front of me walking abreast who I wanted to pass. Just before I could say, "Excuse me," I tripped on a rock and my hand landed on one of the women's shoulders. She screamed like I had pulled a gun on her. Her companions turned around to see what was happening. I don't think that I look very threatening, but I guess you never know. Maybe that bottle of Gatorade that I was carrying in my waist pack looked like a deadly weapon. ("Hand over your money, or I'll squirt you with my Gatorade.") After apologizing for scaring everyone and explaining what happened, we all went on our way. On my way back, I ran into those people again, but this time from the front. We smiled at each other and then I ran back to my cousin's house.
My most interesting running experience was on the Greek island of Kalymnos. I went out for an early morning run after breakfast and decided to get off the road and go up a hill that had a dirt trail. As I was getting toward the top of the hill, I heard a lot of bells. When I got to the top, there was a huge herd of goats with the herders. It was like something out of a storybook about Greece. I got some funny looks from the goat herders because I'm sure that runners weren't a common sight on that island.
When I go on vacation to Italy next month, I will pack my running gear. I'm sure there are some nice places to run along Lake Garda.