My own IP-spending ideas

ARAM reroll purchases. Keep the accumulated ARAM rerolls, but allow for purchase additional rerolls for 750IP (increasing by 250IP per reroll purchased that day) or so.

IP Betting Allow the player to bet flat amounts of IP during ranked matches. Should they win, they'll receive double the amount bet. Should they lose, they lose it all. Also allow betting on friends but make it only available in summoner's rift (ranked). Alternatively, you can have a game mode where everybody who enters has to put in a flat amount of IP. The winning team goes the pot (but remove/halve the IP rewards)

The ability to temporarily own skins. Lets say you've been eyeing a skin for a while now, but the RP cost is 1350 so you're a bit iffy to toss money at it right away. Allowing somebody to rent out a skin for three matches (for double the RP cost as IP) would allow players to try them out and mess around to see if they'll be willing to spend money on it. To prevent people who have loads of IP from constantly funneling it into skins, have a cool-down period of two weeks or so between each test. Only allow for commonly-available skins, too. No legacy skins or skins otherwise unavailable for purchase at the time.

Same thing as above but with the champions themselves. Allow a person to rent out a champion for six matches (for a third of the IP cost). This won't count towards the necessary amount of champions needed for certain game-modes, and an emblem will appear next to their portrait to signify that the player using that champion doesn't actually own them. That way people will be more inclined to try out new champions without breaking their IP wallets.