People still want to be rich. It is a bit of a difficult thing to do with the end of civilization and all, but its a goal none-the-less, and goals keep you going. Not an easy one of course, there is a bit of a currency problem. You can't eat gold, or shoot silver, so despite what the doom and gloom crowd believed before The Event, precious metals are pretty much worthless - old coins even less so since there is a distinct lack of numismatists driving a market. Bills are a bit of a problem - find an old bank or currency exchange, and you've got millions of them.
A lot of city-states reissue their own currency. For most, this just means taking old bills and adding a few extra signatures and embossing. Actually making your own indestructible bill paper and anti-counter-fitting measures is a bit too hard for most places. However, if you want to amass a collection of bills that are worth something, it seems that both Vegas and New Birmingham have their own now, and Tesla probably does too - though they tend to avoid money altogether, and use electronic means when they can't.
Vegas bills - or more officially "New Issue American Emergency Printed Currency" match the old money pretty well, but have new designs on them. A lot of folks call it "nostalgia notes" since the new theme is great human inventions on one side, presidents on the other - so there is no mistaking it for something produced by people breaking into the old mints. The one is an Apollo Moon landing, the Five is the USS Missouri and the ceremony that ended world war two - the rest I don't quite recall.
As you might expect, everything on "NB bucks" or "Cross checks" is a religious theme, getting more ostentatious as the denominations get up. The One is just some hands and a cross, the two has a little church, five is a big one with wings, ten a cathedral, twenty is supposedly the old Jerusalem temple mount, and while I know there is a fifty, I think it might be a bit blasphemous to mention who is pictured on it.
For those of you who aren't after little slips of paper, there are plenty of other things to be seeking. Cars are a pretty common one. Sure, taxes, insurance, fuel prices and so on tried to ruin the allure - they even built entire city complexes trying to render the personal vehicle obsolete. Never happened. Even with the paucity of spares these days, a collection of cars is a real status symbol. Lots of guns or different types of guns are common collections too, but that is often a considered common sense rather than ostentatious and frivolous investment, so doesn't count as being wealthy to many.
Alien artifacts are a mixed bag. They're perfectly willing to trade art objects, or even small weapons. I've got a citizen made knife myself - get a custom fitted hilt, or everything is child sized. Of course, finding more citizen gyro-jet bullets is difficult, so it fits in the impractical category. Actual alien machines or bigger weapons - those are a lot harder to come by as they're almost always destroyed in the process of getting them away from the original owners. Even intact though, they don't do a human much good - so they're rare, but not valuable.
Probably the biggest draw is preserving historical artifacts. No one is really watching the museums these days, so all sorts of priceless artifacts are either going to ruin or being taken. That is probably why they're featured on the new issue bills, because after this, we might not be able to see them again.