I believe your question is in the context of job interviews. Asking right questions can help interviewee getting insight on many aspect of the organization. At the same time it will help interviewer to learn prospect employee's interest areas.
One approach to frame these questions - reflect on the discussion you already had and identify if anything which you want to understand was not part of the discussion. For example - if you care about innovation, asking question on how organizations promote innovations and encourage employees to be innovative.
Asking other general questions to understand long term vs. short term organization goal, employee engagement, organization values can lead to engaging discussion.
You want to ask questions that will provide insight into the workplace environment. You also want to ask questions that will illuminate if the job is a good fit for yourself and the goals you have set to achieve. A simple example is: "What is your favorite thing about working for the company?".