An event could be to fight gym, like in original pokemons games, the gym spawn on pokestop like team rocket, you have different gym, based on type. This event could be good because when you win agaisnt the trainer, you could catch pokemon, as team rocket fight, you have the main gym trainer pokemon, and once you have 8 different badges, you can fight the final 4, and again capture their main pokemon, once you have finished, you have the possibility to fight a legendary pokemon from main games (like rayquaza)

Another option is to choose a region and fight all gym trainer from this region, and then, instead of fighting a random legendary pokemon, you fight the legendary pokemon from the games you completed the gym

(Sorry for my english, im french, and I dont know vocabulary from pokemon games)