If you want to park in downtown Seattle and head up to Volunteer Park metro bus route #10 passes right by the east side of Volunteer Park every 15 minutes. You can pick it up anywhere in downtown along Pike St. It moves over to Pine Street as it goes up Capitol Hill all the way to 15th Avenue before turning left there.
Route #10 passes 4th & Pike in downtown at 9:45am, 10am, 10:15am, etc and arrives at 15th Ave E and E Galer (E Highland Dr.) next to Volunteer Park 15 minutes later.
Here is the Saturday schedule.
Another route to consider from downtown is route #49 which also heads up Pike St in downtown and up Pine Street on Capitol Hill but turns at Broadway Ave and passes fairly close to Volunteer Park. Get off at 10th Ave E & E Prospect St.
Of course another option if you are driving into Seattle from another city would be to park on Capitol Hill and walk to Volunteer Park and then take a bus back up after the rally at Westlake Center in downtown.
