Nick Cave and the Bad Seeds is a hard one to make recommendations for. Um, try Tom Waits, DeVotchKa, and The World/Inferno Friendship Society. Also before Bad Seeds he was part of a band called The Birthday Party which was awesome, totally different sound, old school goth/post-punk. He is also part of a band called Grinderman which I guess you would call Garage rock, good stuff as well. He has worked on a quite a few movie scores too which are all worth buying/downloading.
Blind Melon was just a great 90s alternative band. I really can't think of anyone off top they sound like that you probably wouldn't know about. Their album Soup is one of the most underrated albums ever in my opinion.
I'll let RJ handle Thrice for you...I just worked a 12 hour shift and I'm way too tired to think any harder lol.