For a bit of a side quest, I want my party to go on an errand for a brass dragon in exchange for an item they need. Thing is, I'm at a loss as to what to make them do. Any ideas? Please help!

For anything outside of Eberron, you could send them to clear out a pesky horde of kobalds that have been bugging it, either through zealot worship (driving away the potential guests that brass dragons love to interact with) or pilfering its treasure. Or the item could have been stollen by a rival dragon, and they have to steal it back. The second would be interesting, since I'm assuming they aren't strong enough to fight a dragon head-on.

Alternatively, almost all dragons like music, you could send them out to find a lost song if they have a bard (or anyone who can sing), or have them find a bard who knows the song.

Also an item for an item quest is also good. You need this item, I want a crystal dragon statue, we can trade if you bring me one.

Well, you have chosen Brass dragon and they aren't necessarily evil, but, my favorite ploy is to first surface balance the errand exactly like Silverthorne says - an item for an item.

But after the PCs get to the village or township where the item is located they determine that the item has a magical effect crucial to the area or families of denizens in that area. There are in fact already several factions vying for control or the chance to use the item for ab event or period that is coming soon calendar wise. Unbeknownst to the villagers, the dragon is one of them. Exactly why the item is important or the dragon would want it I leave up to you BUT there should be a compelling reason why some people within the party want the item to go to one faction in the village (not the dragon) and just as compelling a reason why some other party member want the item to go to a second faction within the village (not the dragon). Now that's an adventure!

You can go further. Carrying the item outside its ritually setup area of storage is dangerous in some way and has some random effects besides. It should be a lot of trouble getting it back to the dragon or even just moving it. Why would anyone go through all of this? Well of course the PCs, upon discovering the item's importance look it up in the town's city hall or library (whatever passes for recordkeeping entity). They discover that there is a way to unlock greater potential in a small set of other items by transferring some of the power of this item to the other items (lets say one item of each PC's choice). This also wonderfully diffuses some of the item's far reaching power which will reduce tensions in the village. Now we have an additional incentive only visible to PC's smart enough to do their homework.

Thanks! Those are all great ideas. Ya'll are a great help! <3