First off, great question. I used to coach golf at the Division I level and I think there are a ton of factors that go into a college decision as you said. As a young player, one really needs to be able to look ahead and not just at the school name. The player needs to evaluate their game and be honest with themselves about where they will be the best fit. A highly recruited athlete will of course have lots of options and will be able to pick and choose more freely including looking at the other recruits in their class and determining where they would best fit in. Along the lines of your thoughts, I've organized mine in the order I think they should take precedent.
Again, being honest with your self-assessment is key. If you plan to play professionally or think you might, and honestly have the talent, then academics might be lower on your standards (not that this is how it should be...the chances of making a career out of the game are extremely small without a very high skill level and/or lots of money).
-Coach - This person is going to essentially be your boss for the next 4-5 years. A player needs to understand the coach's philosophy and beliefs regarding the team and be willing to do whatever is asked of them.
-Many people will say go somewhere you know you can play. I don't disagree with that thought, but I also feel that if you are afforded the opportunity to go to a program that might have better players than you, this can really help your game if you are the type of person who can be patient while getting better.
-$ obviously can be a determining factor.
-Location is also a major factor. Do you want to stay close to home? Get away from home? Go somewhere warmer or cooler?
-Academics - I will put this in the middle as it really changes based on the person.
-School size - Are you looking for a smaller, private campus or a larger state-school type atmosphere.
-Tradition - To be honest, I would personally have a hard time making this the bottom of the totem pole if I were in the recruit's situation. Basing your decision solely on the fact that that school has had success in the past is a tough one. The coach may have changed, the players who had this success are likely not all still there, other schools may be getting the best recruits now, etc. Tradition is important if the coach and facilities are the same or better than they were, but basing your decision on the name alone can be dangerous.
I know this doesn't really answer your question about where I would play, but it's just some food for thought.