The computer center is located in the Contemporary Convention Center. You can get to it by going through the doors that are to the left of the main lobby doors. (Right would take you to the bus stop and the side walk to the Magic Kingdom.) Once through the doors take you next right and the computer center will be about half way down the hall way. In February I went to the computer center to do the same thing but it was very expensive. I do not remember how much it was but it was enough that I would not pay to use a computer. I seem to recall that you needed to pay by the half hour.
FYI, I have no idea if the CR will do this (ill find out next week), but most hotel concierge desks or front desks, if you give them your confirmation number will print your pass for you.
For some strange reason when we stayed at the CR last year they would not let us use the computer center (said it was for conventions only), but went to GF and used the one there with no problem. Also, there was no charge at the GF.
You do not need to pay to use the computers at the Convention Center - just go to the front desk and give them your confirmation number and passenger names - they will check in for you, and print the boarding passes - NO CHARGE! No hassle either!
We were flying Southwest, and not using DME, and they still said - no problem!
I went down Labor Day morning at about 7 am, at the Contemporary.