Amazon. With a static site you could even host it in a S3 bucket for pennies a month.
Edit(Your First Project):
Look up hosting static site in S3. You'll find a ton of tutorials about how to host a basic html + css + js site on S3.
Best thing about S3 is you only pay for the storage and bandwidth, so unless he's getting thousands of hits it'll only cost a few pennies/dollars a month. If he's getting so much traffic that it's costing more than a shared hosting provider then he should should be making that money back in spades from clients.
At a high level all you need to do it put your html/css/js in a s3 bucket named after your url and point the CNAME variable of the domain(on godaddy) to the s3 bucket.