Start with your local library and any other libraries in your area, because they should be free to sign up for.

Then there are some that have an annual fee for out of state residents, this article covers many of them. I’ve heard that you can get around this fee at some libraries by picking a random in state address, though I’ve never tried it myself.

Additionally, the Seattle public library allows a free card for anyone in the US under the age of 26, and Brooklyn public library does the same for anyone under 21.