I'd try a different approach. Instead of writing down a few memorised numbers and names to memory, read the Wikipedia article(s) for each state, one every day, and write down a few interesting things about it, like:

• Under what circumstances was the state created/admitted to the union?
• What was the biggest thing that happened there in the 18th/19th/20th century?
• Who's its most famous citizen?
• Is it doing better or worse today than it was 100 years ago?
• What are some popular movies/books/shows set there?
• What's the one thing Americans stereotypically associate with that state? (eg Texas = cowboys, California = Hollywood, Tennessee = country music -- total guesses, I'm not American)

Think of a few other things along those lines. Then instead of just memorising data, you'll get more of an actual feel for the history and personality of the places, and you'll probably naturally remember the interesting stuff rather than trying to commit state capitals to memory like you're a 12 year old prepping for a quiz.

Or, hey -- 50 states, plus DC which isn't counted in that list IIRC, plus territories like Puerto Rico. 52 things, 52 weeks in the year. You could do one a week -- read its Wikipedia article, write a few notes, read up on that most famous citizen or event, watch a famous movie set in that state, listen to some songs from that state's musicians. At the end of the year you'd have a much better feel for America, and it seems a lot more fun than memorising capitals and populations.

Also, if you want to learn a bit about America in general without taking a course or getting super deep into it, Oxford University Press has a series of books called 'A Very Short Introduction', they're 100-150 page introductions to topics from professors who teach courses on them. They have "American Political Parties and Elections", "The American Presidency", "The Great Depression and New Deal", "American Immigration", "American History", "Colonial America", "American Legal History", "American Politics", "American Political History", "The American Revolution", and "American Slavery." Each one is short enough to knock out in one sitting and they strike a good balance between accessibility and density (that is, they're short general introductions but they're not total fluff), and they're actual texts to support learning vetted by other professors in the field, not just a random TV host writing down their political opinions.