I'd say a few of my least well known favourites would be Blind Melon. No Rain is not representative of their discography (www.youtube.com/watch?v=lPzoJCcOMF8
Catherine Wheel's first two albums. They got filed under shoegaze in the U.K but w/e (www.youtube.com/watch?v=b_sHfo2RWxo
Tripping Daisy's I am An Elastic Firecracker is grunge enough in my eyes and a pretty fantastic album.
Then there's also bands like Hum (www.youtube.com/watch?v=gs5nzdDExoQ) and Failure (www.youtube.com/watch?v=G76y-apl3VU who got branded post-hardcore and all sorts of Shit. It sounds like grunge to me, it's 'down' enough to fit the descript.
I'll think of some other stuff when I'm not on my phone taking a Shit but for me, nothing trumps Chains. Saw them last year (yeah yeah no Layne) and it was incredible. Peace
*Edit* Ok, so I'm off the shitter and I've spoken to the lady who has a similar music taste to me. She suggested the following: Helmet (not really grunge but Meantime, Betty and Aftertaste are all stellar 90's albums anyway),
Machines of Loving Grace (these guys are NOT grunge but they have PERFECT 90's production and their music aint cheery.. try 'Concentration' it's 10/10 (www.youtube.com/watch?v=vd74F8kYROg
Godflesh (growing up on one of the poorest housing estates in Birmingham gives you the power to make GRIM music. So it's not really grunge but it's got more than enough of that grit you're looking for. Try 'Pure' or 'Selfless' as some of their discography is pretty hard to get into.
Silversun - she says these guys are an acquired taste and to try 'Lava' or 'Golden Skin'
Afghan Whigs - these guys really aren't an 'album' band but try the songs 'Gentlemen', 'I'm Her Slave', 'Conjure Me' - I like it anyway 
Coroner - these guys were a legendary thrash metal band back in the day but their last album 'Grin' is about as 90's as it comes.
Meat Puppets - try the album 'Monsters'. It's late 80's so strictly before grunge's invention but it ticks the box for me.
She's also suggested some other pre-grunge bands like Husker Du, Giant Sand, The Replacements and fIREHOSE.
If you like metal then I can say there's a hell of a lot of gritty & 'grungey' sounding stuff if you dig deep enough and don't take it too seriously. Try Bethlehem's S.U.I.Z.I.D or Lifelover's 'Konkurs' but don't forget to bring a box of tissues!! 
I'm sure there's some reet good stuff I've forgotten but maybe you could share some of your favourite stuff. Btw I'm not dissing the stuff that was 'big' at the time I just wanted to suggest some things you might not have heard of. Peace!
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