SR-2 is great once you're past Index. Check out the Seattle Randos route for the Stevens Pass Summit 200k for the bypass route on the backroads from Sultan through Index to avoid the nasty, narrow bits. The climb up to the summit has huge shoulders (about a full lane) all the way from Skykomish to the top.
Other great day climbs are to head down to Rainier and do the Paradise climb, or Skate Creek Rd. The climb on SR-410 past Greenwater and through Rainier NP (Cayuse and Chinook Passes) is excellent. If you want long day (3hr drive each way) or overnight, then head to Packwood and try the climb through the Giford-Pinchot NF up to the Babyshoe Pass summit. Bring fat tires (32mm) for that one because the top 7 miles are unpaved gravel service roads.
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