Carrying my bike emergency stuff is a perennial pain point for me. I have to bring it with me when I lock up the bike to avoid theft, but I usually don't carry a bag I can stash it in. Inspired by some bags I saw made by @thenorasaurus, I made a similar one of my own. Here it is in use.
The bag is an ordinary rectangular shape, but the sides aren't sewn all the way up to the zipper. There's some extra room for the zipper flaps to reach around the top tube, so it hangs by the same zipper that keeps it closed.
It's big enough to hold my lights, fix-a-flat kit, pants leg strap, and if I removed the notebooks it would fit a spare tube. Everything I need for my bike while riding around town.