I'd go for Zion and/or Bryce. Grand Canyon is great, but to get down very far into the Canyon is a substantial committment in time (just did a 3-day backpacking trip there in March). Bryce is a climb-down-in experience too, if I recall correctly, but I don't believe it takes as much time to experience it, and it's pretty cool down in.

Zion is my favorite, I think, of all three --- climbing up to Angel's Landing is a hoot if you're not bothered by heights. You could at least get a taste of the narrows, and just getting an overall feel for that park via the bus system might give you a taste of what you want to come back for and spend more time doing on a later trip.

OTOH, just one day might be frustrating there, whereas Bryce could be experienced pretty well in just a day IMO.