Do a search on "free web hosting" and see if there is something that fits your needs.
If you need gigabytes of (free) storage, you can put your files on Google Drive or OneDrive (Microsoft) and make them open access.

What I do personally is use the miserly 20 megabytes of web server space provided by my ISP to run a portal that is basically a collection of links to the very large files that are actually on OneDrive (previously SkyDrive).

I would think that if you are at MIT there would be no shortage of people who can advise you on this.

EHK
Oxford, UK