My office on Maple is basically at the center of your search radius. With your half mile restriction, you will be East of Woodward and the only home I see that meets all of your criteria appears to be more aluminum siding than brick. That house is listed for 225k.
If it could be something other than brick, then you would have 4 more options ranging in price between 160k and 299k.
Expand slightly beyond .5 miles and your options will open considerable.
Actually, this week I sold a house that would have fit your criteria exactly. It was bank owned and had 14 offers on it. My buyer bid cash and considerably over asking to get it and they got an amazing bargain. Those kinds of deals don't come along rarely, but you have to be ready to act quickly and decisively when they do.
If I can be of further help, I would be happy to do so. My family has lived in Birmingham since the 1960's and I do most of my business in this city. Please feel free to contact us.
SKBK Sotheby's International