Safe areas with decent ptices are hard to find on the east side. Willoughby is really nice so south Euclid. Done parts of Cleveland hts are not safe so be careful. I personally just moved from east side to near west side in Parma and i love it! Very affordable, houses are cheaper and better/newer, and the schools district has an excellent rating compared to cleveland hts n south Euclid's adverage. Ive always been east sider but with my new lil one i took into consideration school district ratings also, as school district ratings mirror the community around you!
Parma is a quick commute to east side also, i work in south Euclid takes me 20 minutes to get there!!! And Very close to highway, metroparks, and even the zoo! Its also in cuyahoga county which means free zoo visits on mondays!!!