A huge part of the alternative scene was the grunge movement. Many of the later bands (not Goo Goo Dolls, but fairly certain about Creed) that were part of the alternative movement were hugely inspired by grunge.
I too grew up with this music, and chances are that if you like alternative bands in general, you might find the grunge bands interesting too. Maybe you won't like many of them, but their music is distinct indeed and you might hear their reflections in other alternative bands.
Grunge was the counter-culture answer to the commercial metal and rock bands that dominated the 80s. You know, hair metal, glam metal, those big theatrical bands with tons of makeup, lots of leather, huge crowds, shock value, face painting, etc.
Grunge de-emphasised all the clothing and makeup, and focused more on music. The lyrics mostly spoke about every day life instead of fantastical and/or satanistic themes. Note: the lyrics would still get fairly dark and brooding, often speaking about drug problems etc. BUt it was more connected to real life problems, not about poetic ballads, etc. The clothing too was "grungy" or what a typical blue collared worker would wear. Casual, flannels, jeans, etc. You have to note that this in itself was a big shift from the commercial rock scene of those days. The alternative movement copied much of this ethos.
I might even know why you dislike Nirvana - after all, they ended up becoming what they themselves resented (at one level). A problem which many bands face by the way. Start out by being indie, garage, counter-culture, and end up becoming mainstream, commercial, and all that nonsense.
If you want a true dip in the grunge pool, try Alice In Chains. It takes some getting used to, and be warned - it is extremely dark and brooding, but it is also nothing like you will ever hear. Listen to Down In A Hole, Dirt, and Would. Again, one of those bands whose music you may or may not like, but much of the alternative scene was heavily influenced by Chains.
Other stuff to try out - Seasons (motion picture soundtrack - possibly the only OST that can give you an instant primer into the grunge scene).
Other commercially successful grunge bands
- Soundgarden (with an Indian guitarist! - recommended albums - Superunknown and Down On The Upside)
- Stone Temple Pilots (albums - Core and Purple)
- Pearl Jam (of course! - but you should listen to their first two albums first - Ten and Versus)
If you want to hear one of the very early grunge songs - this one would be it. This is actually not a typical grunge song but there's a ton of history to this song.
https://www.youtube.com/watch?v=HffbME_B7JQ