Cycling is more fun than running for me but exactly because of all the reasons you mentioned I prefer running over cycling. What I also realized is that nothing works as good as running (at least for me) for weight loss if you also change your eating habits (you need to have a calorie deficit in order to lose fat).

For around 9 weeks I managed to go running for 10km every second day and then my two weeks vacation happened. I'm trying to get back in again because I'm extremely frustrated on days I don't go running. I cannot emphasize enough on the stress relieving part. For me it's around 50 minutes of complete peace of mind where the only things I focus are breathing and moving my body.

One thing I recommend is to track your runs because it's fun and interesting to see your improvement over time. Bonus points if you track your heart rate as well. :)