The TriMet's Max light rail is a great way to get from Portland's Airport (PDX) to downtown.

Here's the directions from the TriMet website.

Getting to the Marriott:

Starting from (Airport MAX Station) Portland Int'l Airport MAX Station (Stop ID 10579)

1. Board MAX Red Line to City Center & Beaverton TC
2. Get off at Morrison/SW 3rd Ave MAX Station
3. Walk 0.5 mile south to 1401 SW Naito Pkwy

Travel time: 55 minutes (including 16 minutes walking)

Fares: Adult All Zone ($2.30), Youth/Student ($1.50) or Honored Citizen ($0.95)

Getting to the Hilton:

Starting from (Airport MAX Station) Portland Int'l Airport MAX Station (Stop ID 10579)

1. Board MAX Red Line to City Center & Beaverton TC
2. Get off at Mall/SW 5th Ave MAX Station
3. Walk 0.2 mile southwest to 921 SW 6th Ave

Travel time: 45 minutes (including 5 minutes walking)

Fares: Adult All Zone ($2.30), Youth/Student ($1.50) or Honored Citizen ($0.95) 

Getting to the Hotel Modera:

Starting from (Airport MAX Station) Portland Int'l Airport MAX Station (Stop ID 10579)

1. Board MAX Red Line to City Center & Beaverton TC
2. Get off at Mall/SW 5th Ave MAX Station
3. Walk 0.4 mile south to 515 SW Clay St

Travel time: 53 minutes (including 13 minutes walking)

Fares: Adult All Zone ($2.30), Youth/Student ($1.50) or Honored Citizen ($0.95)

Getting to University Place:

Starting from (Airport MAX Station) Portland Int'l Airport MAX Station (Stop ID 10579)

1. Board MAX Red Line to City Center & Beaverton TC
2. Get off at Mall/SW 5th Ave MAX Station
3. Go to SW 5th & Morrison (Stop ID 7625)
4. Board 12 Barbur to King City (Frequent Service: Buses run every 15 minutes or better weekdays)
    
5. Get off at SW 5th & Hall
6. Walk 0.2 mile southeast to University Place Hotel & Conference Ctr (310 SW Lincoln St)

Travel time: 59 minutes (including 7 minutes walking and 6 minutes waiting)

Fares: Adult All Zone ($2.30), Youth/Student ($1.50) or Honored Citizen ($0.95)