There are tens of thousands of indie bands who would love to have their music in a film of almost any kind. All you need do is find a band that has the "sound" that you want. It's just going to take many hours of sifting through the good, the bad and the ugly to find something very close to what you need. The tough part is to find the right track with great sound quality.
It's also worth noting that you could do all the leg work to track down the "right" track from an independent artist, and they might very well tell you "no", or charge a fee. This is what a "music supervisor" does, because just tracking down musicians and record companies (even if you have a budget to spend) is honestly a lot of work.
You really can't assume that every artist is happy to work for exposure... because most are certainly not. Especially not in this day and age. Unless you're exposing them on a legitimately large platform (in which case you should be paying anyway), most musicians aren't going to see a lot of incentive in it for them. Some artists, (probably if you know them personally) will do it as a FAVOR, but keep that in mind; it'll be seen as a favor towards to, not the other way around.
You will also likely find that most often the artists willing to do it for "free", frankly... suck. Or at least they're "not developed" artistically and technically. The professional people with good songs, that have been recorded well, who've invested $$$ into their craft, are less likely to work for free. Unless, as I mentioned, you're getting a personal favor from someone.
