How would you handle a dinner bill under these circumstances?

I am going out of my way to where this woman lives, instead of the place we had talked about before.. which is actually more like 2/3rds from me (but it's NYC) ... so I am going to her town instead. She will pick the restaurant because she knows the area and I don't.. She's older than me.. I don't know her money situation, but if she sold her house she'd probably net 7 figures from the sale (really expensive town)... so do I offer to pay the bill, or agree if she wants to split it or pay for it? I am not hurting for money, but yeah.. Also before that I'd probably suggest we continue the date maybe in private, I dunno... depending on how she responds to that would also impact how I handle it.

How would you handle a dinner bill under these circumstances?
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