I feel the actual ability to cook is an obvious one everyone wants. But since I'm adding a few others, thought I'd just add this one still.
More furniture options (and counters for corners )
Getting sick so you'll have to buy meds to get better as well as grocery shopping
Being able to design your character's looks (and clothes shopping maybe?)
The sales in shops actually updating. Mine always have the same exact sales on it no matter how long the game is, so I think it'd be fun to actually have it update
Being able to make your own address book and write in it (or have it automatically update) in your home just because I like how it looks lol
Also accidentally murdering someone when defending yourself (like when you use a knife, or if you knock them out too many times in a certain period of time, like in one day). When you murder them you have to try to clean up your tracks to prevent getting put in jail or something.
My more big picture idea:
The ability to receive letters of your own, e-mail, and get callers. This will also go into your home having a chance to be broken into, suspects getting suspicious when you investigate them, possibly even threatening you even if they're innocent (I mean, no one likes having every bit of detail about them known to anyone).
But you could receive letters and calls from people who do like you as well, possibly making a relationship system where you can build or destroy relationships with others. Some people will automatically like or hate you depending on who they know or if they themselves are a bit of a detective and know you will do anything to retire (like investigating your friends and arresting them). If you have friends, they're more likely to share information and let you in their houses for free (as well as possible gifts and maybe coupons?). If you have enemies, they will NEVER share information with you or let you into their home willingly no matter the price, and will be more likely to send threats