Because S3 offers free in-region uploads we were wondering what region The Netherlands is? Specifically Amsterdam. After some extensive Googling I could only find some articles about the newly opened centre in Frankfurt.
I know from experience that Frankfurt facilities mostly focus on the south and eastern parts of Europe so that's why we are not sure.
I suspect you have misinterpreted something you have read.
Amazon Web Services has 9 global regions, Northern Virginia, Oregon, Northern California, São Paulo, Ireland, Frankfurt, Singapore, Tokyo, and Sydney (and two special purpose regions, GovCloud and Beijing).
A "region," in AWS parlance, does not refer to an area of the globe in the same sense in which you are using the word.
An AWS region refers to a collection of two or more "availability zones," which are physically or logically independent and distinct yet are geographically close enough to be interconnected with high speed + low latency fiber optic circuits.
These data centers (availability zones) are what makes up an AWS region. To say that data transport is free "within the same AWS region" means that it is free between services inside AWS, where the traffic does not leave the AWS network and does not leave the availability zones in that AWS region, though it might cross from one availability zone to another, within the region.
If you are interacting with S3 across the Internet from a server or browser that is located outside one of the AWS data centers, you are not, then, in any region.
However... the second issue with your question is that there is never a bandwidth charge for the incoming bandwidth for uploads to S3, from anywhere, so the meaning of free within the "region" is not clear to me.
If you have, say, an EC2 virtual server instance in one AWS region, you'd most likely want to use S3 in that same region, to avoid latency and outbound data charges from EC2 for the cross-region traffic out from EC2 to the bucket (the upload itself would still be free, but outbound cross-region traffic originating in EC2 would not be). Otherwise, choose whichever region performs best for you and your target audience.
Bear in mind that S3 storage and download charges vary by region, based on Amazon's varying costs in providing the services.
http://aws.amazon.com/about-aws/global-infrastructure/regional-product-services