There are three basic types of hikes at Olympic, rain forest, high country and the coast. In early July, the high country hikes may still have a lot of snow, especially this year. There are too many hikes to even try to list but I would suggest driving the Hurricane Ridge Road, visiting the coast at one of several places and take a short or long hike in the Hoh or Quinalt rain forests. You could drive to Port Angeles and stop at the visitor center there to get more information. The Lake Crescent, Kalaloch, Lake Quinalt and Sol Duc lodges are fun places to stay but may be hard to book. There are several campgrounds around the park if you like camping. A good place to go for more information is
http://www.nwhikers.net.