I've lived in the Cincy area my whole life and can help, but I need more info from you.
What are the good and not so good areas of the city? - Are you looking to live in the city, or more like the suburbs or rural area? The gaslight is nice, however, do NOT go outside the gaslight. If you see a place for $500 a month, you're outside the gaslight. Apartments in the gaslight seem to run about $800 mo (for 1 bed). Monfort Heights is nice, but kinda pricey. You could always live in Northern Kentucky. If you live in Ft. Thomas or around there then downtown Cincy is a short drive away. Also, I've found that apartments in Northern Kentucky are more affordable and nicer than apartments in Cincy. Hyde Park is nice (in spots) as well. Clifton is not good, nor Avondale, Westwood, Over the Rhine, Lockland. Many parts of the city can have nice spots and bad spots so you really need to price compare. If it's too good to be true, it usually is.
Where can I find affordable housing? - What is "affordable" to you? Can you give a price limit? And how many bedrooms and such are you looking for? I live in a rural area (Pierce Township) and pay $600 a month for a 2 bedroom 2 bath condo. 1100 sq ft I am surrounded by the elderly so it is nice, quiet, and safe. Are you looking to buy or rent? What kind of commute are you looking for or do you need to be on a bus route?
Do you know anything about specific childcare centers in the city? There are many daycare centers, if that is what you are talking about.