Suggestions:
- reproduce StackOverflow's Markdown Preview editor (notice how they spice things up at time including Math Mode). Today I just saw Typora which is gorgeous but potentially confusing.
- Microblogging ( not just a Twitter client, store the Tweets locally ) -- this is the hello world for Rails and as such FRP tools like React or Elm should devour this (don't also forget Reflex)
- the MTA turntile data set is obvious far for Data Science courses -- create a decent UI for such analysis, also CitiBike
- a zillion other things that should just be better in Elm
- Candy Crush Saga / Bejeweled / 2048
- Crossword Puzzles (such as here). Trivial to code, the challenge is a good User Interface design, separating the wheat from the chaff.
- Elm should be robust enough to emulate (or completely replace) your favorite jQuery or React UI -- try the inspirograph
- I always admired the website of Rafael Albuquerque rafael.pt and even used his designs on my own web page https://github.com/rafaqueque/rafael.pt this can be re-done in Elm (for a more functional)