A realistic dating sim with characters that have realtime lives and interests. For example there's a new movie/play/show/sportsEvent that's out on netflix/streaming/broadcast. They express interest, we make a date. I see the movie/play/show/sportsEvent they are watching at the same time and make comments about the content.
App fixer. Don't like the way the default photo app treats your images? Need your fav game to be playable in landscape mode and not just portrait mode. Use App Fixer.
Something that competes with and obliterates Facebook by just extending Email. Just present my email in a timeline format, allow me to block people who I don't want to get messages from again. status updates would be CCs to all my contacts or only a database entry to a free, non-siloed server. Instant messages would be either on IRC or XMPP within the same client.
There you have it, buddy. Go conquer!
I'd rather kill email.
It's an idea worth exploring further, just to break facebook's monopoly. Even a mail client without profiles, interests and albums but which presents emails in timeline format could contribute to that. I won't pretend it's the ultimate solution, I will just assert that simple ideas lead to bigger and better ideas even if the implementers have to pivot sometimes so it's worth thinking about.