Besides at the Hospital, there's no campground in the city center area. Jantzen Beach isn't far distance-wise, but can be 60-90 minutes at the wrong time of day from OHSU. There's another nice RV park on Marine Drive, about halfway to PDX. But traffic situation will be similar, although at least you have side street options during rush hour.
There is an RV Park in Beaverton behind the Transit Center, but they have a waitlist for RVs. RV Wait List – Mobile Home Corral & RV Park Beaverton, Oregon
Another campground in the metro area is in Tigard: https://roamersrestrvpark.com
Not that close to OHSU, but traffic generally flow a little better than to Jantzen beach in the afternoon. But still up to an hour driving. The good news is you can take the bus to the hospital with a single transfer.
Beware the rush hour traffic in Portland can be every bit as bad as the Bay Area. I highly recommend renting an AirBNB with good transit options, rather than using your camper outside of city limits, if you think you'll be making frequent trips.