Snowy mountains, rainforests, scenic beaches, pretty lakes, waterfalls, ... -- what more could you ask for in a National Park? My family and I had a day and a half to enjoy Olympic in early June. While we were able to visit several highlights, we could have been happy filling at least 3 days.  We visited:

• Crescent Lake -- a very pretty lake that's right along the main highway across the north edge of the park, so you really can't miss it. We didn't have time to do any hiking around here, just stopped to enjoy the views.
• Ruby beach -- a dramatic ocean front landscape! We planned our visit at low tide so we got to successfully hunt for green & pink sea anemones, sea stars, crabs, and more among the rocks and tide pools.
• Hoh Rainforest. Giant old trees dripping with moss. We did the  0.8 mile Hall of Mosses and 1.2 mile Spruce Nature trails. Both were beautiful and very easy hiking. There was more hiking that would have been fun to do here but we opted to visit another part of the park
• Sol Duc Waterfalls.  Again, a pretty easy trail, 3.2 miles round trip to see some very pretty waterfalls. There are also hot springs near here but we didn't visit them and I think you may need reservations ahead.
• Hurricane Ridge, Hurricane Hill trail. You drive up to roughly 1 mile elevation, where you get great views of the glacier-capped Olympic mountains. The trail is mostly asphalt paved, leading up to fantastic views of both the mountains and the sea (and Vancouver Island, etc., Canada). It's a pretty easy 3.4 mile r/t hike, but was a little more challenging due to the fact that big parts of it were still buried under up to 3 feet of snow (first week of June).  Really great views all around, though, and thoroughly enjoyable.

We visited the first week of June, and feel we got pretty lucky with decent weather, just a little rain.  Hardly any bugs yet. We got around with a rental car. I was just blown away by the variety of landscapes you get to experience in this one park.