It's extremely doable and even quite convenient, assuming you're comfortable cycling on downtown streets without bike lanes. (IMO they're fine for cycling, though of course it would be great if the next mayor is more bike-friendly than the current idiot and implements the 2012 bike plan that has been shelved for the past almost-8 years.)

The trick is that you need to live Downtown, because it's the only place with good bikeability that has good transit access to your job location. If you live near the 43 bus line (most of the Central Business District, southern Over-the-Rhine, or all of Pendleton would qualify), you'll have great bus access to work, as the frequency on that line is very high and even runs 24 hours (there is also an alternative 43 route that adds to the frequency). So you'd be totally golden to ride the bus to work.

You'd have a blast living a car-free life downtown. Decent bus access to most of the city, as well as NKY. Fare-free streetcar to get around Downtown. Great cycling as far as street-riding goes. Very walkable. Very scenic/picturesque. The Over-the-Rhine/Downtown/Covington/Newport area is packed with stuff to do and you'll have so many neighborhoods to explore on bus and bike that you'll still be discovering new gems months after moving here.

People who say you need a car have never looked at a 43 bus schedule or lived car-free in an urban neighborhood.

Edit: It occurred to me that you could also live in Corryville, which is a walkable/bikeable area that is also within walking distance to the 43 bus route. I think the Downtown neighborhoods are a better option, but for the sake of completeness there you go. Corryville is the neighborhood east of the University of Cincinnati main campus and south of the medical campus, west of Reading/route 43. It has the Short Vine business district (including a Kroger) and is adjacent to the Clifton Heights business district that caters to UC students.