I used to be like you. Want to have "good" training, top name, big city, bla bla bla. You see, your day as an anesthesia resident is dependent on which attending you work with. One attending will crush your soul no matter what you do. Or there is an attending whom you know you will have a good day even if you screw up. Not to mention, you sometimes get yelled at by the surgeons because they think they are god and you are just their "gas passer." Do you really want to be in a high-strung environment, working until 6pm when you are NOT on call to relieve CRNAs, having no free parking or free lunches, no moonlighting opportunities, then go ahead go to those places. People have their own measures of happiness.
As for Columbia,.. the institution, not the country.. NYP is a FINE institution, a 2400+ bed hospital with high acuity. Excellent ICU training, for one. They even have a 1 on 1 training for ICU ARNPs, which is almost unheard of in other institutions. UW's Harborview level 1 trauma center only has 400+ beds. It has a lot of trauma because Seatte-"ites" can't drive ****. I really do not think it is comparable there. But, both will give you excellent trauma training given their variety of cases. Sinai has moonlighting. I forgot which other ones have moonlighting. If you get paid $50/hr for staying late in the OR, you will be a happier resident... I'm just saying...
As for location, I cannot really say about the southern states because I have never lived there, but sorry dude, NYC beats Seattle... big time!! You can go anywhere from NYC by train, by car, heck by plane. You can go to Abu Dhabi on a direct flight from JFK if you like. You can easily drive to Connecticut, Boston, Providence, NJ, PA, MD etc from NY.
From Seattle, the next "big cities" are Vancouver, Canada and Portland.... mehhh, they are just like any other american cities (yes, including Vancouver), rather nondescript, I'd say. California, however, is a nice and easy access from PNW. If Mt. Reiner is your thing, mehh we have Adirondack in NY, plus we have other ski resorts easily accessible in our neighboring states. Seattle's beaches have no friggin' waves, good luck surfing there... paddling maybe.
Anywho, good luck in the match.