Blaine said:
Nope, sadly, you can not lower bounty unless you go to jail or pay off the fines. My record bounty was in the 80k range... I killed every guard in Imperial City.
If you join the Thieves Guild, you can have the higher ups clear bounty. I think it costs 1/2 the actual bounty fee, or some junk like that. Depending on your bounty, it'll be a better alternative than obviously paying up the full price, or serving your sentence, as skill levels reduce depending on the bounty value.
Lanien, at level 20, you can do all the Daedric Shrine Side Quests. These yield.. interesting items(Such as a staff that makes a clone of the target NPC, that follows you around and fights for you)
As well, the main story calls for one to be used, removing it forever. Just a tip, while the story says Azura's Star, any of the Daedric Artifacts can be used, but Azura's Star is by far, the most useful one. It's a reusable Grand Soul Gem(the second biggest type after Black, which are the only soul gems that can capture human souls.) So for the love of god, use one of the other Artifacts instead, as Soul Gems are used for Enchanting equipment and refilling charges on enchanted weapons, only carrying around Azura's Star is a lovely thing.
For some info on the items you obtain from these, check out
this page.
Figure out which one you wouldn't mind parting with, and use that one for the story quest. That sites a good reference for info overall too.