Google App Engine is great & free for low volumes of traffic. I use it for my crypto dashboard: https://priceeth.github.io/
Github pages if it's static enough, or for any static part.
If the amount of data is small / static-ish, and can/needs to be changed by non-tech people, I've also used Google spreadsheet. Example: https://hasgluten.com
FaaS/Serverless will be a good starting point for something like this, so either AWS Lambda, Azure Functions or Google Cloud Functions will be good enough.
The free tier of AWS Lambda gives you up to 1 million calls per month. You could use this for the actual fulfillment of your data. Paired with AWS API Gateway (1 million calls for free per month for the first year), it seems that you could do this relatively cheaply.
The only thing I haven't accounted for here is if you're querying against some sort of database, which would incur additional hosting costs.
^ important. If you're trying to provide free access, I always seek ways to mitigate cost. If the API can be slowly updating, like once a day or w/e, then I stick everything behind a static CDN or something such that it should cost you next to nothing. Just a small CPU somewhere to build the JSON endpoints per update cycle.
Github pages if it's static enough, or for any static part.
If the amount of data is small / static-ish, and can/needs to be changed by non-tech people, I've also used Google spreadsheet. Example: https://hasgluten.com