Summoner Hub?
I'll apologize in advance because this has probably been suggested before, and because my Canadian citizenship card demands so.
I think it would be cool to be able to log in to an mmo-like 'hub' map, where you could walk around as a summoner and queue for matches with an in-game ui. The visual style and perspective could be the same as SR, but instead of pushing mid, you could be running around Piltover in yordle-sized summoner robes.
Something like this would give players a better way to interact with each other, while right now it's limited to friend's and match-mates. Instead of 3 / 5 man teams, you could join a 'guild' and queue with people around your rank, similar to the arena system in WoW.
I might create a playable prototype as my next semester-long game dev. project, depending on what people think.