Currently WL, however I've been living in Portland for a while and can offer some thoughts on this (especially if you're not very familiar with the city).
Most convenient place to live would be the South Waterfront, because you could walk to the RLSB and/or tram every day. However, the SW is also hella expensive. IMO the best places to look for a spot are in: (A) Lair Hill (B) Brooklyn (C) Moreland-ish (including East ML, West ML, Creston-Kenilworth and Sellwood) (D) on Marquam hill (E) anywhere else that's within a short walking distance to the yellow/orange line.
(A) Lair Hill is also walkable to campus, but adds 10-15 minutes. Cheaper options than SW.
(B) Brooklyn is over the river, but walkable to the Orange line which has a stop at the RLSB. ~15-20 minute commute total. Also very easy to cycle from this neighborhood w/very little road sharing.
(C) This general area is a little further out than Brooklyn, but you can still cycle to campus or catch a bus/train easily. More housing options & you'll feel more like you're in the city.
(D) There are apartments on Marquam hill west of campus. Kind of dated. Were very affordable a few years ago, not sure what the rent looks like currently. This option is just as convenient as Lair Hill, but it is more removed from the rest of the city. So you'll be living/breathing/sleeping in OHSU all the time.
(E) The yellow/orange line is the train that stops at RLSB. It is fast & reliable. If you don't find anything you like/can afford in the above - look further north or south along the Y/O line.