If you're willing to drive that far, may I suggest looking into Bend, Oregon as a possible destination on your trip? The Cascade Lakes/Central Cascades are about half an hour outside of Bend, with endless hiking possibilities, such as a summit of South Sister.
Oregon Hikes - South Sister I made it about 2/3rd of the way last summer before the elevation started getting to me. Even a hike to Moraine Lake (shown in the photo on the link) is worth doing. If you want to see impressive mountains, the Central Cascades is the place to do it.
Here are some pictures from our trip to that area last summer:
Broken Top
Mt. Bachelor (Bachelor Butte)
South Sister with Moraine Lake in the foreground
Not my pic, but a great aerial view of all Three Sisters:
Also, if you want an impressive view of the Willamette Valley, the best to be had is at the top of Marys Peak in the Coast Range:
Siuslaw National Forest - Marys Peak Marys Peak is neat in that on one side, you can see all the way to the ocean, and on the other, you can see all the way to the Three Sisters. On a clear day, you can pretty much see all the major peaks of the Cascades in Oregon. The hike to the summit itself is fairly short because there is a road that goes almost all the way to the top, but there is a really nice hike to the summit by parking at Connors Camp and taking the East Ridge trail to Tie Trail and then going up to the summit.
You might consider a loop that has you driving up the Gorge to US 97, down to Bend, bumming around the Central Cascades for a couple days, then taking US 20 back over the mountains to the Willamette Valley. Marys Peak is about 45 minutes from where US 20 hits I-5, and is on the way to the Oregon Coast if you wanted to see that.
The chances of rain in late June are slim to none, but come prepared with a good shell nonetheless, because it's Oregon and you never know. It's unlikely that it will rain so much that you get stuck in a hotel room during that time of the year.
If you're looking for some good books full of great hikes, here are some titles I like: