For most games the gates begin opening two hours before game time. For promotional give away days it is highly recommend you are there around that time. The lines start forming around that time and as the saying goes, the early bird gets the bobblehead.
Arriving early also has more perks than just scoring a free gift on promotional nights. Batting practice will likely be going on as you're finding your seats. Rule number one for the saavy baseball fan is to always have a glove. Make your way to the right field bleachers and the ushers will let you try and snag a homerun ball until batting practice concludes. If you hope to score an autograph, early before the game is likely your best opportunity to do so as well.
Safeco has several small attractions and sights to see before or even during the game. Let the kids run off some energy at the Seattle Children's Hospital Playfield located on the main concourse in centerfield. Just a short walk away from there is the Mariners Speed Pitch where you can test your arm and see where you stack up against the pros. In section 105 is the statue of the late voice of the Mariners, Dave Niehaus. He sits with his back to the field offering a beautiful backdrop for you to capture a picture with a Seattle legend. The new Ken Griffey Statue in front of the main entrance also is a great photo opportunity, however there will be several people lined up for a photo with The Kid. The Mariners Hall of Fame and the Baseball Museum of the Pacific Northwest is located on the main concourse from sections 135-141. Take the time to learn about the history of Mariner baseball and celebrate the greats in Mariner history. If you're looking for new Mariner gear, the Mariners Team Store is located on the west side of the stadium facing the street. There are also many shops inside the stadium with a large variety of jerseys, shirts, hats, and souveniers.