The Austin Public Library uses the Overdrive interface for ebooks. And, given Austin's size, I suspect they have a sizable collection of ebooks, too. Get yourself a library card and borrow library ebooks for free from any physical location where you have internet access.
Note that these books are downloaded in their entirety to the Kindle (or to your laptop and transferred to the Kindle), so you're not reading online. In other words, you need the internet only during the download, not while reading. Further, the file sizes of ebooks are surprisingly small, measured in a few hundred kilobytes, not megabytes. They download very quickly, even over a marginal internet connection.
:)
Lynn