Good question! Depends on what you define as “near.” I know lots of folks paddleboard on the Willamette River…which isn’t right in McMinnville, but isn’t that far away, either. There are multiple places to put in/take out on the Willamette. I know people paddleboard from Wallace Marine Park in Salem, which is maybe 30 minutes from McMinnville.
Another place you might try if you want a contained location with no current to contend with is Henry Hagg Lake. It’s especially good for paddleboarders because it’s divided into two sections, one of which is a “no-wake” zone where folks who want to paddle on non-motorized craft can do so safely. It’s about 40 minutes north of McMinnville.
I would suggest you talk to local paddle sports outfitters — they’ll probably be more than happy to give you the rundown on the best spots. Oregon City-based eNRG Kayaking is a reputable local business that does guided trips and rentals on the Willamette River and around the northern end of the Willamette Valley.
Good luck and happy paddling to you! I recently tried out paddleboarding myself for the first time and had a blast.