You might wanna check out Songkick: https://www.songkick.com - it does exactly that and it's awesome.
I just tried it, for the bay area it said there were 1887 concerts, then gave me no way to facet the search results by genre, venue etc. I tried the search box, which, confusingly, is right next to the "sign up as an artist". The search results despite the bay area being set as my location showed me concerts in London as the first result.
I wouldn't say songkick is anything like awesome.
Your use case should be accommodated too, granted, but it's not the direction they're currently headed.
Based on the GP's (and your) report, the search box should be replaced with a freeform text field or somesuch that lets you input artists you're interested in, and a button that subscribes you to notifications.
TBH, my http://www.last.fm/events is more useful, I find.
I don't think a website is. But each to their own! (I suspect this is the overuse of the word "awesome" that reduces the really "awesome" things to "super extra awesome".)