Look at the braking surfaces closely for signs of any deep scratches due to the pads galling and picking up rim metal and at the same time embedding pad material or dirt into the deep scratches. A good pad material will wear the surface down smoothly. If you have rows of deep scratches then it's time to switch brake pads to get a longer and more even rim life. Again the old saw suggesting Koolstop salmon or at least switching to Koolstop pads will help a lot.

In the meantime a Scotchbrite pad will clean up the rims pretty well by shaving down the worst of the peaks and digging the grunge out of the deeper grooves. Use it with soap and water and some elbow grease. I don't like the idea of the brillo or SOS pads since the steel wool breaks down in use and all those steel fibers floating around seem like trouble waiting to happen if they don't all get washed away well.