Well i go to the international district on a semi regular basis and have had no problems. i frequent the uwajimaya/kinokuniya shopping center and they were OC friendly in all my past visits. i have also walked around the area to visit other shops with no problems to report.
As for the U-district. like any where else your right to OC on public property is protected, private property owners can ask you to leave or cover up as is there right and you must comply of face tresspass charges.
Remember that your in the most liberal anti-gun city in the state and probably close to the most anti-gun part of that city when you head towards the U district or capitol hill. be prepared to defend your rights intelligently-download the OC pamplet, learn your rights under state law, as well as terry V ohio(no right to search, siezure or demand of ID absent a crime), deberry V US(no legal terry stop for lawful carry of a firearm) and Glick V commonwealth(police may be audio and video recorded with or without thier concent).
And remember if your approach by law enforcement because some liberal flipped out that you would dare defend yourself... the first words out of your mouth should always be-
"Why am i being detained officer?"
Here is an example of a well educated OCer-