Only some indie. Also some punk in various punk subgenres (hardcore, post-punk, post-hardcore, etc), and some industrial.
But back to subject.
There is no excuse for liking Avril. None. I'll say this again. N.O.N.E.
Avril is Britney Spears in Hot Topic duds. If she wasn't hot (and really, I hate to say it, she's really NOT hot), no one would even pay her attention. Hell, you even admitted that her music isn't even trying to be decent, but is rather an avenue for her to pimp her body out. Even being "attractive" (hint: it's all makeup), the only people who take her seriously are 13 year old (and younger) girls who think that wearing heavy black eyeliner and wearing a studded belt makes you a "rebel." I'm in my early 20s. Girls half my age just don't interest me enough to make me suffer through 2 hours of shitty music. I'd rather go to a show where I'm going to meet REAL punk chicks. You know, the kind who will break your balls in the moshpit.
And just because it's free doesn't mean you have to see it. I see bands for free all the time at local bars. And normally, they suck, but I've definitely seen a lot of good bands for free at local bars. The Swayback, Tin Tin, Matson Jones....I've seen all these guys live, for free, in tiny little venues, hell, I've gotten to chat with some of these bands after the shows even. And it's good music (I love the shit out of Swayback. I don't care if they're local or not. They are awesome) and a good scene.
Plus, the beer's cheaper.