Three individual bands I'll recommend you.
Mother Love Bone: The band that pre-dated Pearl Jam. Mother Love Bone only had one album and that was Apple. They were suppose to be huge, they were suppose to be the next big thing. Geffen wanted to marketed the band as the Guns N' Roses of grunge, commercial wise. None of that happened though due to the death of lead vocalist Andrew Wood. He died of a drug overdose. Although Mother Love Bone seems to be a forgotten part of history in the sands of time, they live on in the heart of grunge fans everywhere. The band had a unique blend of glam rock thrown in with the Seattle sound. Something unusual that sounds rather good (IMO anyhow).
Soundgarden: I see that you didn't want metal recommendations. I also see that you like some alternative rock. I'll assume you've heard Soundgarden (even bigger chance due to their ties to Guitar Hero lately), but I want to recommend them anyway. Early Soundgarden had a stoner/doom metal splice of sound to them. Later Soundgarden was more along the lines of alternative rock. Soundgarden is a band that I recommend you get all their studio albums.
Thin Lizzy: In my opinion, the most underrated hard rock band of the 1970's. People have heard "Jailbreak", "The Boys Are Back in Town", and "Whiskey in the Jar" at least once. Aside from those three big commercial hits, Thin Lizzy was VERY consistent with material. They may have had a couple of average albums in between, but I can't say a "bad" album. My personal favorite album from them would be Vagabonds of the Western World.