I just have one main, one medium, and one small idea.
1) More in-depth audition process.
Instead of clicking on our character to start an audition and then only having three options, I'd personally like a more interactive menu/choice. Maybe in the same menu where there's the option to do tours and elections, there can be a tab for auditions as well. Then, we can select what kind of audition (Local, Regional, National) and also how many girls we get to choose from (5, 10, 15). The more girls and the larger the scale of the audition, the more expensive.
The only problem I'd see, is how the game determines when we can hold each type of audition. My idea for that is to have us gain "audition points" or some other generic name. We could gain the points every week or every day; Similar to how we have to wait a certain amount of time to hold another regional or national audition, it could take that long (and that many audition points) to do a 5 member audition of that scale. So, if you don't do auditions that often, you can save up your points and do one big audition once a year (which is what I prefer to do). For the beginning of the game, maybe the player will have infinite points, so they can freely get their beginning group going. Another thought would be maybe we'd have to research the larger auditions.
2) Medium idea - Seeing the election results before they're announced
I can't tell if the election results are completely based on total fan count for each girl or if it matters what type of fans (hardcore vs casual), but I just think it'd be nice to see who's going to be announced before hand so when I put in a girl I'm trying to push up, I'll know if I even have to.
3) Small idea - skippable concerts
I just want to have the option of skipping the whole random chance bottom right circle thing.