We parked on the street within a block of the museum.

Your best answering this question would to ask the museum

The Portland Airport (PDX to casual travelers and KPDX if you are a pilot) is about 15 miles / 30 km northeast by north of the downtown area near the Portland Art Museum by road. Taxi cabs are not cheap in Portland because the cab numbers are seriousl;y constrained by government regulation. Little competition. Uber does not currently serve Portland, though may be doing so after 1 April 2015. Because I live here I don't usually stay in hotels, so I have never had the occasion to take a hotel shuttle to / from the airport. I simply do not know which, if any, of the downtown hotels have an airport shuttle service. Perhaps a bit of research / e mail directly to one of the downtown hotels will yield an answer. As to rates, $ 120.00 including local taxes is doable but difficult. A friend about a little over a year ago stayed at the Portland Marriott on the river front down town for a room rate of $ 90.00 / night in September, 2013. Her company was doing a multi day event and the relatively low rate may have had something to do with the event being located at the hotel. The Portland Convention and Visitors Bureau supposedly has an online private chat application with a staff member who can advise on hotel questions. Google Travel Portland. I am not allowed by Trip Advisor to directly give you the URL for the website. The "big" hotels downtown are The Portland Marriott; Portland Hilton; Heathman; Embassy Suites; Mark Spencer; Monaco; Benson. Those are not in any particular order of recommendation; they are just the local hotels I recall off the top of my head. A more extensive list is available Trip Advisor. I would send you the URL for that Trip Advisor page, but Trip Advisor bars folks answering questions from transmitting URLs for web sites, including Trip Advisor's. I think you best bet may be getting on the Portland Convention and visitors Bureau site and doing a "chat" with one of their paid staff members. The International Date line always causes me much confusion, and I do not readily know the time difference between our two locations. You may need to watch out for that in contaction the Visitors Bureau. I do know they are closed on Sunday, so today ? / tomorrow ? may not be a good time to contact them. I wish I had better direct answers to your question, but this should get you on to the people who will have answers. I think the combination of $ 120 / night plus shuyyel may be a tough one to meet. I hope you do enjoy our city.