Our favorites/recommendations - The North Bend Bakery; Saints & Scholars Irish Pub; Huxdotter Coffee; North Bend Bar and Grill; the Elk Fields between the cities; downtown of either city; and any park by the Snoqualmie River!
In July, we recommend using the White River entrance to the park and driving the route to Sunrise. July is a beautiful time of year to be in the Park and has numerous hiking trails to be explored. This entrance is located about 1.5-2 hours from Seattle's Eastside.
Our recommendations for visiting Seattle include the Space Needle, Pike Place Market, the Museum of Pop Culture, the Seattle Aquarium, and the Seattle Ferris Wheel. The city has a bunch of great parks, restaurants, and museums worth visiting!
We see Mount Si everyday as it sits right above North Bend. There is a longer hike to the top that has incredible views from the top! Just be prepared for switchbacks... It's beautiful from the bottom too and there are parks around North Bend with great views of the Mount Si and the Cascades.