Grünerlřkka is usually considered the hipster area of Oslo, not Aker Brygge Aker Brygge is the corporate high-end business area: overpriced restaurants with good views.
As you are arriving Saturday afternoon, I would recommend eating somewhere in Grünerlřkka (around Birkelunden) and stroll around there, fighting the jet lag. On Sunday, unless you have particular cultural interests, I would do the ordinary outdoors tourist things.
Vigelandsparken is a must (and free). A new, very popular activity, is walking the roof of the new opera house.
Except for a few December Sundays shops are closed in Norway, so probably no Sunday shopping for you. At which hotel are you staying?