I have lived in Tremont for 4 years and really like the area. Yeah the winters are cold and long in NE Ohio, but the summer and fall are amazing coming from TX.
Tremont and Ohio City are both good options on the west side. Would also add in Detroit Shoreway or Lakewood, but those are further west. There are pockets of nice areas on the east side, but it is very hit or miss so would just be careful - Cleveland Heights has some nicer areas as does Shaker Heights. Around campus tends to be fine as well. One thing to consider is the east side usually gets more snow than the west just due to lake effect.
Cleveland has a small town feel to me (coming from Houston), but it has all the amenities of a large city - 3 pro sports teams, world class orchestra, museums, etc. Pretty happy here and don't really have plans to leave.