I like a first date to be something public & a bit generic. Like dinner, or lunch, or going somewhere casual where other people are, but not with us, like a park or festival.
I agree about the arriving in separate cars. I want an escape pod. Plus I don't want someone I don't know at my house, even if only for a short time. Going to the guy's house for dinner or movies is completely out of the question.
I want to be in a comfort zone where I feel in control of my environment.
If a guy ever suggested going to a cooking class for our first date, I'd have to decline the idea, possibly decline the whole idea of a date with the guy. It would be a huge indication that we'd have nothing in common.
That's the kind of stuff for a later date, after you know the other person's interests.
I've been on a number of double-dates with friends (either his or mine). In every case, there's never been a second date. They were extremely uncomfortable for me. I felt like the others were watching us get to know each other & in a way, interfering. Instead of more comfortable they were just plain awkward.