Stock market: Okay, hear me out. I know the game is too short for long-term stuff, but that's not the point here. Invest your eddies into shares of a megacorp and use the stockholder influence it gets you to gain access to top-tier equipment not available on the street: next-gen cyberware, experimental cyberdecks and programs, weapons so dangerous that simply knowing about them scares the drek out of the CDPD, or even something as simple as custom-ordered clothes. Combine this influence with your street rep, and it could lead to a whole new series of gigs concerning corporate espionage, sabotage, blackmail, and assassination.
Screwing with the sheep: Feeling bored? How about planting drugs on some random gonk, dropping an anonymous tip to CDPD, and sitting back to watch the fun? Or slipping a grenade on somebody and watching it blow up in the middle of the street? How about something as simple as hacking some nearby corpo's bank account and liberating a few eddies for yourself? In Night City, you're either predator or prey; we should be able to get out there and feed on the weak if we choose.
Breaking into random buildings: Maybe I don't want to but some piece of hardware from a vendor and the trash I'm finding on gang goons' bodies isn't worth my time. Why can't I break into a gun shop or a warehouse and lift some gear for myself if I want? Or maybe I just feel like raiding the neighbor's place for some free beer? Think of the adventure possibilities of raiding some place and finding some widget I could ransom back to some corp (the Flathead for example?), info I could use for blackmail, or even something that sends corporate hit squads after me?
Custom coloring for weapons and equipment: Not for nothing, but some of us like simple color schemes for our stuff. I should be able to take the gun I use with the nausea-inducing neon magenta color scheme and redo it in basic black, or color coordinate my clothes so I don't look like a paint shop threw up on me.
Random, deliberate attacks on you: Nobody stays at the top forever, mainly because the higher you go the more people there are gunning for your spot. As your street cred goes up, your rep should make you a target for people looking to make a name for themselves by taking you down. Naturally, they don't all have to be serious challenges. It could be played for amusement to have some knock-kneed gonk with delusions of adequacy thinking he can take you down and falling on his own face in the process.