One simple option is to go for games. They can always use several devices, such as mouse, keyboard, timers, graphics card and (depending what you do) the RTC.
Another option is to go for a "music composer" application. For instance, you could write (using the keyboard and mouse) a song(note frequency, duration) and then let the computer speaker play it.
You could also go for a "clock/calendar application". It could draw a clock in the screen(which might be harder than it might look if you draw an analog one on the screen), and then let the user adjust the time of the day(saving the changes in the RTC). The clock could also include alarm and some ticking sound. As for the calendar, you could also allow the user to create "events" in the calendar, which could work a bit like alarms.
You could also try to write your own "notepad"-like application. This would require having a working GUI(write area, menus, etc.). This could either be in text or graphics mode. You could detect the keyboard being pressed to add character, handle CAPS LOCK(giving you the opportunity to mess up with the keyboard LEDs). You could use mouse position/clicks to change position in text editor or trigger menus. Then timers to have the blinking caret in the text editor. Clicking a disabled menu option could cause a short speaker sound to indicate an invalid action.
I'd recommend writing most of the code in C, except for little bits in Assembly. ISRs are a good opportunity for Assembly code.
Regarding state machines:
- Games can have many states ("Main Menu", "Playing Game", "Pause Menu", "High scores") with well defined transitions between states.
- A music composer could have some states too("Stop", "Pause", "Playing")
- A clock application could have states such as "Show Clock", "Show Calendar", "Alarm Message Box", "Event Message Box", "Event Message Box With Pending Alarm.
- The notepad application could have states such as "Editing Text", "In Menu" or "In Message Box")
Most of the devices you mentioned can be accessed with interrupts. Unfortunately, I can not think of good opportunities for polling...