Server Architecture for hosting Java PLAY application in the cloud
The setup looks good. I would however make one change: your large up- & downloads. As mobile speeds may not be ideal, have your app serve long-running requests is something you should avoid as this will needlessly tie up server threads. Instead consider having users upload and download straight from S3 using presigned URLs. You can then later add CloudFront to the mix when it makes financial sense to do so.
R53 will work just fine for picking the best server(s) for each end user.
For EC2 consider having an ELB + Auto-Scaling Group setup. Even just for a single instance you get the benefit of permanent health monitoring and auto-respawns. If you expect more load you can then auto-scale based on your expected bottleneck (cpu, network i/o). This will give you a more autonomous and robust setup than manually having to scale up and down based on your own monitoring analysis (even though the scaling part is very easy if you stick with immutable infrastructure & blue/green deployments like what Boxfuse offers).
Your focus on vertical server scaling might not serve you well on AWS. I would start thinking about horizontal scaling of app servers behind an Elastic Load Balancer, and possibly look into Elastic Beanstalk.
I'm not sure you can setup a read replica in another region via RDS, you might have to set that up via MySQL servers running on standard EC2 instances. And even if you can, that's going to be some expensive and high-latency data transfer.
If file uploads and downloads are all you are worried about, you just need to put CloudFront (Amazon's CDN service) in front of your application, and allow it to handle file uploads and downloads via its global edge servers. You could even do this without moving your entire application into AWS. I would recommend reading this blog post as a start.