What's a meal without a bowl of miso soup, right?
OK, regarding your wakame, it is dried? If so, it can be stored in a ziplock bag. Just keep it away from moisture. If it's fresh, I think it is best to use it up. The most popular (in my household anyway) way to use wakame is to toss it with some cucumber sliced paper thin and flavour it with rice vinegar (Sushi Vinegar or if you are in north america, they now sell rice vinegar "dressing" that is juat vinegar with some spices and herbs). Once prepared this way, it can be stored in your fridge for a few days.
Some of my my favorite things to put in miso soup are eggplant, mushrooms (Shiitake, Maitake or Shimeji), Broccoli and mochi.