"Why do senators have a role in appointing executive branch officials and judges?" is a sample question that would befit a senator. The senator should be able to articulate that the reason is that their input prevents the appointment of unfit candidates, who might be appointed due to their family connections or presidential favoritism.
With race a perennial topic of conversation, a suitable question might be to ask about the senator's level of satisfaction with the state of race relations in the United States, and how it informs the senator's political views. Another serious topic is global warming, so a good question might be whether the senator feels Americans will have to cut back on their energy consumption to prevent future environmental problems.
Jobs are always important. Ask whether the senator has a plan to increase jobs, or to stimulate job growth, and to state what it is exactly.
Virtually everyone agrees that a lot is spent on government waste and abuse, and, therefore, the government must get rid of this waste. Ask the senator about what some potentially wasteful programs the government is spending taxpayer money on, or that are at least open to abuse and fraud. Follow up by asking what the senator intends to do to eliminate this spending.