Basics about the political (e.g., form of government), cultural, economic (e.g., trade/currency/black-market wants), and social makeup of the kingdom (e.g., class system/hierarchy). Also religion(s) and brief highlight of any distinctive beliefs of the kingdom's people.
How their system of law works (e.g., is there a sheriff watching for malcontents, or is there a secret army killing strangers?).
List of major cities with one-line descriptions.
List of neighbors, perhaps with quotes from their citizens about the country in question.
Are these the sort of suggestions you're looking for?
p.s., are you able to share templates of sheets you currently use?