So as we know rock band 4 is coming soon on consoles so that made me miss a lot taptap games.. Tap Tap Revenge 3 was in my opinion great game with good online/social features (you were able to chat while waiting the song to start, chat rooms). Maybe in the one day...
Have you tried Groove Coaster? I think it's pretty good. You do have to buy a decent amount of the songs, however. Most of the songs are also in Japanese, too.
Demon's Score was fantastic. Theatrhythm was awesome, but got pretty pricey coz of the monetization. The Rayark titles are also some of the best on iOS. You can also check out Planet Quest which i think is awesome with a $1 premium price to get rid of the ads.