There are several teams in the area who have dedicated training set aside, but like Darius pointed out, usually they are team only training events and so they are not talked about on the public forums. I know SOTA does both indoor and outdoor training (especially leading up to the Lions Claw Events). In the past they used some land North East of Vancouver for outdoor training, but recently I believe they have located some new fields for training. They also used to use rent Oregon Airsoft Arena, late night, for their CQC training.
I know teams such as SpecDet1, SOTA, APST, Mithril, RAC. 5, DRAT, Phantom Fury, and a several other local teams rely heavily on teamwork and employ military tactics on the field.
As for specific tactics; SWAT, USMC, ARMY, etc., most teams find that using a mixture of what works best for them and what works best for airsoft is what works best in the field. Because airsoft and real steel are closely related we can borrow nicely form those that came before us, but they are also different enough that you have to modify your usage of some of the tactics for best results. Since in airsoft we are not usually restricted by ROE or acceptable loss ratios (because we have never ending supply of re-enforcement) we are allowed to play with the tactics in ways that the Military wouldn't.
I am a pretty serious player and have been looking to up my game.
It sounds to me like you were sucked into Airsoft, like may of rest of us are, with the enjoyment of the game and the allure of something Mil-sim-esk, but as that "something new" excitement wears off you are still seeking more from the game. You find yourself surrounded by First-Person Shooter junkies out on the field who head toward the sound of plastic death while talking about their Kill to death ratio. Much of what is going on in Airsoft in the PacNW lately is Basic Airsoft. The games tend to be more basic styles like sector control with the main game play being force on force action. They are tailored to players who are interested in getting into airsoft, or who have been playing for a while and enjoy just going out to the woods and shooting people. You will generally find a larger populous of younger players and a lot of these players are within their first year or two of airsofting. Mil-sim is a style of game play that has been around for years but has had some trouble maintaining a large enough following in this area to make for compelling game play. Many think of it as the next level of airsoft. Milsim generally restricts the use of high cap mags, and the games are more focused on teams completing their objectives to overcome their enemy. Mil-sim events can range from an event with more structure to help create more Military stylized game play (objectives only being available for a short time, teams working toward competing objectives) to events where your unit combines with others to march as a battalion, trigger ambushes, setup an FOB and patrol the perimeter. Mil-sim events like Lions Claw are done on large scale AO's with huge groups of people where as most local Mil-sim games will be a smaller scale, less players, but try to achieve a similar style of game play. And many milsim games try to incorporate both Outdoor and MOUNT style game play where available.
If by a pretty serious player this is what you are looking for, then you are in luck my friend... There is an upswing focus on MILSIM in our community, with groups like Milsim west, and APST's new field we should be looking at getting some pretty good MILSIM events locally. Also Lions Claw started an event series last year out on the Oregon coast called OP: Trade Winds.
However if Milsim seems like a step beyond where you are at right now, don't fret. Guys from SpecDet1, SOTA, APST, Mithril, RAC. 5, DRAT and Phantom Fury are easy going guys many of us started airsofting years ago, but most of us remember that we all started airsofting for similar reasons. If you see us out at games feel free to talk to us, ask questions if your interested in what we do, or if you want to find out more information about out teams, it never hurts to ask.