What do I wear for this date?

I'm setting up a first in-person date with a guy I've been talking to online. It's going to be a full-day thing, or at least several hours. Take the train into DC and wander some museums is the idea.

I don't want to be too dressed up because I feel that would be overkill, plus we'll be walking a lot so I want my sneakers. But I do want to look nice.

So what should I wear? (No comments on underthings please.)
What do I wear for this date?
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