Unfortunately, theater in Seattle over July/August is usually fairly slim pickings, due to most of the major houses being in the off season, and don't really start up until September. Rent is a brand new self production put on by the 5th Ave though, so there may be some interest to see what's done differently. Our other large theater house is The Paramount, which only hosts touring musicals, and doesn't have anything coming until Wicked in October. they do keep busy with concerts there between shows.
On the play side of things, Intiman Theater is trying to stage a comeback after their financial disaster that had them scrapping last season. They are showing four different shows in repertory (Romeo & Juliet, Hedda Gabler, Miracle! (a new show by sex advice columnist Dan Savage (who what also the subject of the off-Broadway musical, "The Kid")), and Dirty Story by John Patrick Shanley). I've heard pretty good things about the first three shows.
Museum wise, the Pacific Science Center has the last US stop of the King Tut exhibit. If you have any interest in other types of music, the EMP (Experience Music Project) may be of interest. I think they have three exhibits right now on The Rolling Stones, AC/DC, and Nirvana. Connected to the EMP is the Sci-Fi Museum, and they have three exhibits going on also (Avatar, Horror Movies, and Icons of Science Fiction). The Seattle Art Museum has an exhibit on Australian/Aboriginal art, and their regular collection is pretty interesting also.
Also the Seattle Great Wheel (our ferris wheel) has just opened up on the waterfront, which is a pretty good place to explore in conjunction with Pike Place Market. If you are here during a weekday, it isn't too crowded and touristy.
Xanadu! Can't cry on cue!