June Multi-day Trip

My wife and I would like to do a multi-day backpacking trip the last week of June in Washington State.  We are experienced backcountry campers but have no experience hiking above 3500 feet.  We will fly in and out of Seattle.  Our itinerary is fairly flexible; our only commitment is to be in Vancouver, BC, July 4-7.  I need advice on trails and loops that will not be snow or ice-covered.  I would also like to avoid heavy mosquito or blackfly activity.  The trails along the coast of the Olympic Penninsula look interesting as does the PCT on Vancouver Island.

Advice or references are greatly appreciated.