The water is still pretty chilly. I normally float from early May through October, but rarely go to swim, so don't take my word for good places to swim, I take people for fishing and camping trips.

On the Clackamas you can do Barton park to Carver, which is pretty easy and about a day. There are a couple spots to swim, but I haven't seen any rope swings in the past few years. My kids started taking their own raft at 12-years old. I've done it on an inner tube many many times. It is a pretty easy safe float.

On the Deschutes I usually do a 3-day float from Warm Springs to Maupin (+50-miles over 3-days). There is some pretty big water in there so be aware. Not many spots to swim in, but there are the occasional eddies.

There are also day trips from Harpham Flat to Maupin, and you can drive up to where you put in. I never swim that area of the river tbh. People do though.

The Klikitat in WA has pretty decent floats. I normally park a vehicle near Stinson flats/Leidl South, float to Soda Springs (I think is the name), camp, then get the vehicle the next day. It is a decent drive from Portland. Plenty of spots to swim, but there are some rapids and fast moving water.

White Salmon is a kick ass +3-hour float in glacier run off water. I love rafting it, but I wouldn't recommend it for novices. Wear a dry suit or at least a wet suit. Husum Falls will wake you up ;) Not for beginners.

There is the Trask out towards Tillamook, but that is mainly for fishing. You can swim all over that river, might piss off the fishing folk. You could do this river in a life jacket.

Of course the Sandy is there, but people like to keep that a little secret :P