The near east side has been on the upswing for many years now, however it is going really slow. There are many homes in the area that need completely gutted, or are vacant and abandoned.
Clintonville is a good place for homes that were built between 1920-1960. They are quite different than the homes you would see in Old Town East or Victorian Village. There are some larger, brick homes on Oakland Park and North Broadway and streets to the north of North Broadway toward Whetstone Park.
Depending on your price point, there is a nice area adjacent to Victorian Village that is still affordable. (harrison west)
Also, you may try an area such as Grandview for older homes in a nice, safe area. Excellent schools.
Westerville has a nice downtown with older homes and good schools as well.
If you plan to start a family, you will likely want to stay in an area with good schools unless you plan to send your kids to private schools. All downtown areas such as Old Town East, Victorian Village, Harrison West and Clintonville fall into the columbus school district.
You can research different neighborhoods on my website below.
Best of luck with your relocation,