Right off the top of my head I can think of two examples of aliens based on cats: Larry Niven's Kzin, whom I've read about in Paul Chafe's novel, Destiny's Forge, and Anne McCaffrey's Hrruban from Decision at Doona.
There's something about cats, isn't there? Having two new kittens at my house, I can testify to this.
Okay, so what about making them into a group of aliens?
My thought is this: don't stop with physiology and its immediate consequences.
With the feline physiology you get great hunting capabilities and a carnivorous diet. But in case you were thinking that these aliens would only eat raw meat, think about the little kitties eating kibbles in your house. If they have an advanced society, they would also have a sophisticated sense of cuisine, at least among the wealthy. Maybe raw meat would be a delicacy - or maybe it would be associated with poverty, because these people couldn't afford fire to cook. Either way, it should have a localized cultural meaning.
So then, what about social structure? A lot of times people will come up with structures that are elaborate and cool but somewhat arbitrary relative to the species in question. That's fine, as long as you can make your felines fit into it without going against their native ways (and you can always alter the felines!). However, if you want to match more closely, you could always work with a very social group of felines, like lions. They've got prides with dominant males and hunting females; that would be fun to work with.
I'm going to challenge myself a little by working with housecats - or at least, a group of cats that is very territorial, typically not hanging with other cats unless they are siblings or mates. This can still translate into a societal structure for a civilization.
Imagine a society of semi-nomadic feline hunters that guarded its core territory, yet possessed a superstructure of civilization and government based largely on the interactions of mates and siblings. An individual would have a compound where he/she lived with a mate and their juvenile children, but siblings would be welcome and would probably live in territories nearby. Those territories would be linked to the first by blood ties to create small interlocked communities. Intergroup marriages would take on great importance, especially between larger linked groups - like the marital interactions of the European royals. At the same time, siblings would have very close relationships and would add to the possible links. It might be that the only way to get "into" a rival group would be to marry off one of your daughters or sons, because then that other group would not be able to deny access to that person's siblings, and thus information might travel.
I can see thorny political plots growing already. And therein lies the story.