Where are the best places to hear local live music in Cincinnati?

Fountain Square music: http://www.cincinnatiusa.com/Attractions/detail.asp?AttractionID=559

Bogart's on Short Vine in Corryville still has live music after all these years: http://bogarts.com/

Mad Frog on McMillan: http://www.themadfrog.net/

The Ambassador in Oakley also hosts live shows

The Redmoor in Mt. Lookout has live events: http://theredmoor.com/sectionroot.aspx?sec=m

I also love the open air fun of music on Fountain Square as well. Here's a list of 2012 live music events.

Many bars and restaurants in Cincinnati play local music, especially on the weekends. My personal favorite is the Blind Lemon in Cincinnati, which offers a beautiful outdoor patio and local music every evening of the week: http://www.theblindlemon.com/. Some other bars known for hosting local performers are the Northside Tavern, Arnold's Bar & Grill, and the Blue Wisp, a jazz bar downtown.
If you're looking for something outdoors, most local festivals like Oktoberfest Zinzinnati and Taste of Cincinnati include live performances. Finally, I highly recommend Fountain Square downtown. Local bands perform there even when there's no festival going on, and the atmosphere is always festive and exciting. Check their website for dates and event times: http://myfountainsquare.com/.