Throwing the VPC behind cloudfront is probably the best course of action, if your site is static I'd recommend looking into S3 + Cloudfront for hosting it. It's

Throwing the VPC behind cloudfront is probably the best course of action, if your site is static I'd recommend looking into S3 + Cloudfront for hosting it. It's basically free, and great if your site is mostly static. I run a few scheduled jobs on Lambda to pull some data for my site and it comes out at basically $0 every month.