I just got back form a 3-night 4-day trip from Clarno to Cottonwood this past weekend. This was my 5th trip down there, and I like it better each time. There are numerous fantastic campsites, it just depends on how you break up the number of miles/days. Clarno to Cottonwood is around 70 miles, and when the water gets low it is a loooong trip. I prefer going down there in April to get higher flows to reduce float time. This year it was in the 4-5k range and I wouldn't want to go much lower than that without adding another day. By June, you will likely need a full week that includes some significant oar time, if it is still feasible at all. Clarno Rapid, about 5 miles below the launch, becomes an unrunnable rock garden (at least in a raft or drift boat) at low flows, but is easily portaged with a canoe or IK. Like mentioned by others, the winds can be brutal.
There aren't really any must-do hikes, but pretty much every camp features a nice side canyon or ridge to climb up for perspective. While not really a whitewater trip other than Clarno Rapids, it is really an incredibly beautiful canyon for the entire length. While parallel to and not very far east of the Lower Deschutes, it is MUCH more scenic and has much better camp site options, other than the last few miles above Cottonwood where the pickings get slimmer.
If you have a Garmin gps I have river miles and some of my favorite camps as waypoints. If interested, send me a PM and I can send them to you (or anyone else who wants them, for that matter).