Yup, I live in the East Side and the housing stock is 1, 2 and 3 family homes - my street has all of these and lots of kids. (There were not a lot of kids when mine were little, but there are now, so it can be hit or miss.)

If you want to be able to avoid the highway to and from the hospital, look at the part of the East Side closer to Fox Point and/or College Hill and proximity to the Point Street Bridge. If you don't mind using the highway, look in the part of the East Side near the Rochambeau Library; west of Hope Street will have cheaper rents.

I note people are advising the north part of Edgewood, but one caveat would be that there are a lot of absentee landlords renting to Johnson & Wales students. This can also be true of the Fox Point area, but College Hill is still convenient to the Point Street Bridge, and has fewer absentee landlords and therefore rowdy students.