After you finish de story there are still some things to do. You can do one of the main 3 activities (i discovered so far):

• catching messenger birds: i think there are 10 in total out of which you can set up 5 to get items for you. The birds are ususally found in the round ares where you had fight during the story.
• getting pearls: there are 30 in total and you find them almost in every area you visited. Of course this mission begins during story mode. The reward for finishing this is a material used for item (forgot the name) that makes Substitution chakra free temporarely.
• the cursed dolls: of course this is the most interesting side quest because you get to fight most of the characters in the game. After the game ends, you can set up your team (get what character you want and what tema memebsers you want) and hunt the cursed doll. Of course you can do the other two mission at the same time, because you have to walk around all over the map to find the doll.
• some other small quests: i did several of them, but they were kind of easy and not really that interesting.
• of course you can always get the collectables which cost money or story fragments and memory crystal which you also pick up along the way.

If you use the luck shrine on frog mountain you unlock Sage Naruto character which is really cool. Also the cursed doll for Itachi is really cool to fight as it is rather chalangeing. Rain village is kind of useless, aside from the cursed dolls there.