I don’t wear a wrist watch — years of working and hobbies in which items on the wrist or hands is dangerous killed that habit. However, I still kept a digital watch because I need the time, stopwatch, and timer functions. I stumbled onto this kids’ watch for $12. It has all the features you would expect from a digital watch: time, alarm, timer, illumination, and water resistance to 50m.
My first one lasted 4 years before the spring on the clip failed. The timekeeping functions still works fine, so its now my gym watch. I replaced it with the identical model. I wear it on my belt loop most days, if I am out hiking with a pack I clip it onto the shoulder strap. As for the broken one, I will either carry it or use a silicone band to keep it on my water bottle.
It seems to usually be found online for about $20 which still puts it a half to a third of similar watches. It may not be stylish, but it is a nice durable utilitarian watch.