Any suggestions on things to do in one day in Quebec City?

Hello TBU! :)

I'm currently in Montreal, and visiting Quebec City tomorrow morning with my beau. Due to a tight schedule, we have only one day to spend there, so I am hoping a few of you might have some suggestions for lovely (inexpensive!) things we could do while there, like sites (I do want to see the Chateau Frontenac!) and cafes, views, etc.!

Thanks so much...