The nearest airport is at Portland International Airport (PDX) , which is northeast of Beaverton; see the link for more details.
Taxi fare is about $63.00 from the airport to Beaverton Transit Center to include flag fall & tip.
MAX red line is the most direct & economical mode of transportation to Beaverton from the airport.
From Portland, the fastest is to go west on Sunset Hwy (US Hwy 26) and exit at Canyon Rd (OR-8 at exit 71) or the next one at Hwy 217 (OR-217 at exit 69A) to exit 1 (SW Walker Rd) or 2B (Beaverton Hillsdale Hwy / Canyon Rd) to get to central Beaverton. If coming from I-5 northbound from Wilsonville, Salem or other places south exit at Hwy 217 (OR-217 at exit 292B) to exit 2B (Beaverton Hillsdale Hwy / Canyon Rd) to get to Central Beaverton. Washington Square Mall (mentioned below under 'To Do') is off of exit 4A (SW Hall Blvd) if going south on OR-217 and exit 4B (SW Scholls Ferry Rd / OR-210) if going north along OR-217.
MAX by TriMet  runs frequent light rail (MAX) trains out to Beaverton from downtown Portland every 10 to 30min. The 'red' line train goes from the airport through downtown Portland to Beaverton while the 'blue' train continues to Hillsboro from Beaverton in one direction and to Gresham in the other via downtown Portland. The "train station" & "bus station" are at the Beaverton Transit at 4050 SW Lombard Blvd just north of SW Canyon & Lombard in a central location.
WES is the bigger heavy rail commuter train operated by TriMet going down to Wilsonville through Tigard & Tualatin.
TriMet also operates buses in the greater Portland metropolitan area. Bus #20 (Burnside), #54 (SW Beaverton Hillsdale Hwy/OR-10) and #58 (Canyon Rd/OR-8 & US-26) goes to/from downtown Portland. Bus #52 (to PCC Rock Creek  along SW Farmington & 185th), #53 (loops through nearby residential & industrial areas along SW Lombard, Allen & Arctic), #57 (goes to Hillsboro & Forest Grove along TV Hwy/OR-8), #76 (to Tigard & Tualatin), #78 (to Tigard, PCC Sylvania  & Lake Oswego), #88 (to Willow Creek Transit Center through the SW suburbs along SW Hart) and #61 runs only during weekday rush hour to/from the hospitals on Marquem Hill just south of downtown Portland.
Columbia County Rider goes up to Scappoose and Saint Helens from Willow Creek Transit Center  and PCC Rock Creek. The Willow Creek Transit Center is linked to Beaverton by the #52 bus (traveling along 185th) or the 'blue' MAX train going to/from Hillsboro.
Tillamook Transportation District Rt #5 stops into the Sunset Transit Center (north of Beaverton) on its way to Tillamook from Portland. The 'red' & 'blue' line MAX trains connects Beaverton to Sunset Transit Center on their way to/from Portland.
Yamhill County Transit Area Rt #44 goes to Newberg and McMinnville from Tigard along OR-99W (Pacific Hwy) while the 46s goes to Dayton. To get to Tigard Transit Center  from Beaverton take the #76, 78 bus or the WES train.
The immediate areas around Cedar Crossing Mall , Beaverton Transit Center and old town Beaverton are compact enough and "walkable" by foot if getting here without a car. Other areas beyond are typically suburban with everything further apart which will require a private automobile to get around efficiently. Otherwise Trimet do provide all sort of buses to various places in and around Beaverton from both Beaverton & Sunset Transit Center hubs which are also MAX (light rail) stations.
Some of the activities in Beaverton include various malls including Washington Square, and Cedar Hills Crossing (formerly Beaverton Mall). Both of these malls contain many activities such as great food, including fast food, or formal restaurants. Washington Square recently built a Cheesecake Factory, which is always a popular place to dine. Both malls have movie theaters along with stores that fit anybody's taste. There are many beautiful parks located through out the Beaverton area that are frequented by many people. And, of course since it is the NorthWest, there is a coffee shop on every corner.
Jin Wah in a strip mall off of SW Canyon Rd & SW 117th at 4021 SW 117th Ave, Tel: 503 641-2852. Serves great authentic Chinese food and Dim Sum (at lunch time). A block over from the Beaverton Transit Center.
Buffet Palace on SW Center & Hall Blvd at 12570 SW Center St, Tel: 503 526-8888. They serve all you can eat Chinese food, sushi & crab legs (dinner time only) for $9.25 Mon-Fri afternoons from 11:00AM to 3:30PM; $14.49 on Mon-Thu evenings from 3:30PM to 10:00PM and $15.99 on Friday evenings from 3:30PM to 10:00PM and all day weekends from 11:00AM till close. Great value for the money. Or buy to go and eat for several meals.