Here are a number of ideas off the top of my head I am a long term player and GM of cyberpunk so eat this and like it.
-Style over Substance - This is huge and should allow players to represent their in game choices with style. As technology sufficiently advances a character may choose to purchase a cyber arm or leg that seems to have an "old school" or "first generation" look of Russian cyberware for example that is still every bit as efficient as modern ware.
-Choices Matter - Even choices of gear, weapons etc may attract unwanted attention in certain areas. Choose your gear wisely, and be even more selective about your friends. In an open world game you have a huge opportunity for roving factions... as such you may easily be able to haul around that Assault Cannon in the Combat Zone but you are not going to get away with that in the super secure Corp Districts. More importantly you may need the good will of local: Gangs, Yakuza, Law Enforcement, Corpsec, Mafia, or Union etc to walk freely in certain areas. Until you have gathered the good will of the controlling interests you may find yourself harassed, or worse...
-Player Housing - What is important with Cyberpunk housing is that it is temporary, and even home can be dangerous. You could be overrun at home... you want to check your bed for grenades for example, because when you lay down it just might blow you into the ceiling... in fact what is that dark spot on the ceiling? Maybe it is the previous resident who got sloppy. Living is about keeping your head above water and to most people it is a grind. Everyone wants a piece of what you have but those big scores can elevate you out of the struggle long enough to forget you are one of the little people. But you just might lose your edge...
-Keeping your Edge - This is a HUGE motivator for those who live on the Edge. It is the motivation for getting more cyber, and for walking that fine line between Elite Op, and Cyber Psycho. Walking the line for entry level tech and upgrading that tech to the latest Ultraware.
-Walking your own Path: Being an edgerunner means you don't have to take peoples crap... It means you don't punch a corporate clock and you march to your own drummer. It means you don't hold a day job because the people that do are wage slaves. You risk, blood, bone, and brain matter to live the life of the wolf. You may have a pack at times but you are still and animal that can't be domesticated.
-Being around you is dangerous: For your enemies, for your friends, and for everyone that gets caught in the middle. Sometimes you try to make the world a better place but that usually means dumping some truly despicable person in the river.
-Heists: Edgerunners do Crime. Let us have some fun blowing some things up, and getting away with the loot. Maybe I can have an insertion from an AV on the 50th floor for a VIP bag and tag. Maybe I can knock over an armored truck... but then it's time to find my Fixer.
-Fixers: I don't want to be a fixer... all of the time. But I would like to be one some of the time. And I should be able to make some loot getting the right gear, from the right guy.
-Ripper Docs: These are essential. Get me a black market implant slammed into my anatomy from a guy who insists on eating a sandwhich while he does it. Or better yet maybe this Ripper Doc is a Ghoul and he cuts me a discount if he gets to eat my leftover flesh parts.... good job for a Ghoul, and I don't need the meat anymore anyway.
-Cyberpunk is dark: Don't softshoe it... I might get screwed in more than one way by any person.
-It's the future, Gender/Race/Sex are flexible. on that note...
-Species is Flexible too.... with modern tech, maybe I am a part a subculture that has itself modified to look like a Cat Person, or a gang of bikers that are snaked up. ;-) Maybe I can't play their reindeer games unless I look like a reindeer.
-Don't be shy on gun effects. When I shoot someone let it look like I shot them... if I shoot them with something big... well that's why that explosive ammo has a premium price tag. Also, if I shoot someone in the leg it should look like it, limping and flopping over or being spun around when rounds slam into them. Most people just lay on the ground and look at the hole when they get plugged... they don't keep charging on unless of course they have some mods.
-NPC reactions: If I am on a shooting spree regular people should notice... most people cover, and run like hell. Maybe there is a hero in the crowd. Maybe someone calls the law... Maybe I can intercept that call with my tech...
-Netrunning: This is an absolute MUST. I presume you guys are all over it, but basically when I hit the net, I want to feel like a digital god in raining terror upon the unwary nodes of the people... don't over complicate it.
-Multiplayer I think this could be done exceptionally well with multiplayer and frankly Cyberpunk is at the end of the day and RPG that favors team work. Why not do something truly impressive and have someone moving in the Net and providing overwatch for those on the ground. That auto drone just got hacked and is now eyes in the sky for your team... remember to tip your Netrunner. The Combat Medic will be keeping you stapling you back together in the Van as you hope you don't bleed out before you get paid...