There are two flights a day from BHX-Vienna with BA. There are lots of other flights within Europe also, but they are on various European carriers so I don't think your bags could go all the way without re-checking if you are coming in from the States. Check out the BHX website on the first post above.

If your business takes you to London, then struggle through LHR/LGW, but if your final destination is more than 20 miles North or North West of London then you should consider Birmingham.