I went to Oregon last summer, we didn’t ride out of Portland itself but we did ride nearby in the Mt Hood area which is about an hour out of the city.
I would recommend 15 mile trail but there are others in the area: kneble springs, 8 mile, surveyors, gunsight, dog river.
There are no doubt local rides out of Portland but the closest that got repeated mentions was Sandy Ridge but there was a race on there so we went to Mt Hood instead.
We had our own bikes but I am sure there are places to hire. Advice on where to ride seems to be a big part of the shop scene so a good starting point. And no matter how many GPS tracks we had we always seemed to end up buying the map of the local area – also available in the bike shops!
I don’t there is a huge amount of good trails immediately near the city. As above Hood River is good. If you could get yourself to Bend and to speak to Don Leet who runs Sunnyside Sports he could show you miles of peachy trails. Mackenzie at the Willamette Mountain Merchantile in Oakridge. There are miles and miles of trails around there too. Have a look at Waldo Lake and MacKenzie River Trail.
Portland itself is a great biking city. You’ll love it.