Luxembourg

It's a pretty, pleasant, under-appreciated little country. With just a day, you will obviously be limited in what you can see (even in a small country). The capital is pleasant, although not exactly "grand" like major European cities. It's set next to a deep gorge, so there's some interesting views. The Ducal palace is kinda cute, in a storybook way.

I liked Vianden, a short drive away. A cute town in a small valley cut by a river river, with an impressive castle perched over it all on a hill nearby. What's not to like?

I would go into the countryside. We stayed in the capital 30 or so years ago, and loved it. Then about 10-15 years later we went back, and it had changed dramatically, and not for the better. Everything I was looking forward to seeing was either no longer there or had been ruined.

If you are driving and it's not too far from where you are staying, look up Vianden and Echternach.

I found the American Cemetery very moving.