Grog Shop (Coventry), Mahalls (Lakewood), Happy Dog (Detroit Shoreway) are my usual spots to find good local music, especially punk rock and indie rock. Beachland Ballroom (Euclid) is also good with two venues one large one small. Mahalls has two venues in it as well.

Also shout-out to Blank Slate in Elyria for a great really small venue.

The Winchester is also on the westside and gets interesting acts occasionally. On the Eastside is the Beachland Ballroom and Tavern and the Grog Shop. Is there a specific type of music you are interested in? Oh also the Foundry has metal on the westside