One of the benefits of investing in Cleveland proper, along with lower property taxes, is no POS. I especially steer clear of Cleveland Heights as an investor, due to their strict POS, relatively low values in many areas, and high taxes. If you can find the right neighborhood of Cleveland proper to invest in, the local government will mostly stay off your back, and your life will be a lot easier. I'm particularly fond of North Collinwood.
Some cities that have POS are more investor friendly than others. Some will go out of their way to make your life difficult. Here's how I'd rank them from least to most investor friendly:
1. Cleveland Heights
2. Shaker Heights
3. South Euclid
4. Bedford Heights
5. Maple Heights
6. Euclid
7. Garfield Heights
8. Willowick (dye test)
9. Eastlake (dye test)
10. Wickliffe (dye test)
11. Lakewood
12. Parma
13. Berea
By the way, Brook Park has no POS, but avoid at all cost as an investor. The building commissioner and building department are awful to deal with.