I'd love to see the calendar/event scheduler in game, it should then be in sync with the phone.
I'd also like to be able to see/chat with FC (not just in phone, but in game).

Right now the phone app has been a complete letdown, and it ties into some disappointment that I've had with Stormblood as a whole. I hope that Yoshi-P and team are working hard on something, big, and special. I've shared those ideas and will continue to do so.