I always go to a bar. Its not too formal, because nothing feels weirder than being on this really romantic date with a girl you just started seeing, and there's alcohol, which always helps.
You are way behind the times, buddy. You need to treat her as an equal, while knowing when to hold a door open and when to not ("I don't need a man to control when I can enter or exit a building"), when to pull out a chair, etc. But paying for the meal is definitely on the list of stuff you're still expected to do.
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