As far as the medical community is concerned, yes Cincinnati is conservative. As far as I know, there are no birthing centers that allow midwives to practice without an ob, but I may be wrong. I hear that Dr. Bowen is a good choice (OB) for someone wanting a more natural experience, but I wonder how loaded his practice is since he is sort of one of a kind. I am still looking for a natural family doc, no luck.
I am a Cincy native, so for neighborhoods, I am very familiar with the whole area (in and outside the city limits). I would steer clear of the City of Cincinnati. The schools are terrible, and even the magnet schools, although reported to be great on paper, are not always the experience that you might want for your kids. I went to Walnut Hills for all 6 years - it is a cross between a northeastern prep school and an urban public school. My friend's kids went to SCPA (now Erich Kunzel School for the Arts) and were attacked on more than one occasion waiting for the bus. Cincinnati especially the area near the hospital is very dangerous. My cousin worked CCH until his close friend got attacked in the parking lot. Just be careful - I could list many more very close encounters.
A 2 acre lot is going to take some looking, especially if you want to stay close to the hospital. By the way, are you working at the main campus or Liberty? If it's Liberty, you will have more options to choose from if you want a larger place. West Chester and Liberty Twp are Lakota schools which are pretty good especially in the earlier grades. Mason is also very good schools. If you want a nice family community with very good schools closer to the city, check out Wyoming (I lived there for 10 years and sent my twins to school there from 3rd to 12th grades - there is nothing I can say negative about Wyoming) It is pretty central to everywhere, close to 75 - took me about 12 minutes to get to work downtown in heavy traffic. You might not find 2 acres, but some lots are larger. My tiny yard was big enough to garden in. Montgomery is a nice area too, with many properties being resold as "tear-downs" where small houses on large lots are torn down and a bigger nicer house is built. Montgomery is Sycamore schools - highly rated. For prop taxes, I think you will find Montgomery, Mariemont, and Wyoming fairly similar and close to what you pay in the City of Cincinnati.
That's all I can think of for now! Let me know if I can help you in any way and good luck with your move...