Lots of good riding down around Rainier, though I'm not sure what will be open by 5/16 -- Skookum Flats and Noble Knob are two options along 410 that are great rides.
Just got back from mountain biking in Hood River and can highly recommend it. Hood river is a great town to hang out in. Recommend Brian's Pourhouse for eats at least once while you are there.
Go highway 20, camp at Early Winters for Free and rent bikes from Dave at D-Tours two miles from your campground in "downtown" Mazama. Trails will be dry on that side, also much less threat of rain.
