Try Arabellas Landing first 253-851-1793. They usually have quite a few slots and are centrally located.
Next would be: Harborview Marina 8513948, Murphy's Landing Marina 851-3093, Peninsula Yacht Basin 858-2250, Pleasure Craft Marina 253-549-6639.
Anchoring is also a good choice. Just look for spots north of the Public Dock and near the Seattle Yacht Club out station. Lots of folks do that. And as mentioned by others, if you cannot find a spot to tie up, the public dock has quite a few spaces for dinghy tie ups for boats anchored further out.
Hope you can find a spot. Lots to see in Gig Harbor and several good eating places.
Good Luck. Gary and Rosalie 253-857-7049 Gig Harborites.