Wow, all these ideas are interesting and promising, it's a shame the developers don't seem to care that much...
Look, I have some ideas too:
1. Locations
Just as there could be a beach in Riverbank and the brothel, it would be cool if there was a set of mountains and dense forests as a 3rd explorable area in the game (Or a simple state park) where we, the player and NPCs, could camp from time to time, it could even work as a school activity...
2. Mechanics
Your best friend is distracted, what do you do? Give him a pat on the back! - Did you find someone you've been missing terribly? Jump on them and give them a big hug! - Or are you one of those guys who likes to harass girls who seem like potential prey? A little grope here, a little slap on the butt there... (Or maybe just wanting to tease your friend/best friend or girlfriend, just a silly thing.)
3. Jobs
So far there are only 3/4 jobs available in the game, namely: bar waiter/waitress, supermarket cashier and generic fast food attendant. So... Depending on the character's gender or physique, we could work in city delivery as a delivery driver, as a stripper in a brothel, or simply as a babysitter (or pet sitter as well).
4. Storyline
The player's parents should have more impact during gameplay, like: "Mom?! Dad?! What are you doing here?!" + "Hello daughter/son! We came to your apartment/house to visit you only to be a terrible nuisance! Being extremely lazy, arrogant, and completely ruining your romantic relationship! If you even have one! Did you like it?"