Of course. It is not at all a dumb question, and it's a great position to be in. Here is some advice on how to proceed with the negotiation, based on your situation:
Be straightforward and confident. The CEO has opened the door for this conversation and has specifically asked what you need. This is a clear invitation to give a number. Your calculations are solid and based on real-world costs of living, which is exactly what a high-cost-of-living location demands. There's no need to feel awkward about it.
Give a specific number, not a range. Based on your calculations, you have a clear need for $150k-$160k. It is better to state the higher end of your desired range to leave room for negotiation, and you can justify it with your cost-of-living analysis. Stating your "absolute bare minimum" of $130k upfront gives them an anchor to negotiate down from, which you want to avoid.
Don't justify your number with your personal situation. While your family's needs are the reason for your number, the CEO is interested in the value you bring to the company, not your personal expenses. The best way to justify your salary request is to anchor it to market rates for the role in the Boston area and the value you will provide to the company. You've already done the homework on the cost of living, which implicitly supports your number.
Keep the focus on the value you bring. Frame your response in terms of your excitement for the opportunity and the skills and experience you will contribute. You can say something like, "Based on my research into the cost of living in the Boston area and the value I know I can bring to this role, a starting salary of $160k would allow my family to thrive and would enable me to focus fully on contributing to the company's success."
The fact that the CEO came back to you after you turned them down is a strong signal that they want you and are willing to pay for you. This gives you a lot of leverage in the negotiation. Be polite, professional, and confident in your worth.
