It actually came to me today while I was on the morning walk testing my new mirrorless camera in sunrise conditions. When I finished I was about 15 minutes from home and way back is rather boring photography wise - road, cars, houses, more cars etc. A bit shy in the beginning but I started to pick up the pace... faster... and even faster...
You can actually run with this thing! If you're confused - I'm talking about new mirrorless cameras. The Sony a6000 with 16-50mm lens (24-75mm on full frame) is the size of my palm (I'm quite tall though), weights 450 grams and the quality of the photos is DSLR like. It should fit easily into one of those waist bum bags you can get even for few pounds, I'm actually waiting for one to be delivered to test it out.
So, whether you were already jogging and missed your camera looking at the beautiful scenery or (more likely) you want to get more fit but just couldn't get to do it - now you have 2 reasons. There's my tip for you.
Open google maps and look for all the nice places (parks, interesting buildings etc) in your area. Get out of the house just before sunrise (if you're early bird) or sunset (a lot easier for majority of us) with your mirrorless in the waist bag. Now you have best light for your photography and you're losing those pounds - 2 birds with 1 stone.
And here's me, getting fit with mirrorless in my hand on bmx track - without bmx bike. Bear in mind, my silhouette is stretched by the morning sun, normally I look a lot more... proportional :)