Another yes for staying in Palermo/Monreale. With just one day, you will be hard-pressed to choose from among 6 or 8 highlight things to see or do.
And, definitely another big no to renting a car, you won’t need it, and traffic and parking are horrendous.
Do be diligent with your valuables and belongings. While people are friendly and helpful, and I myself had no problems, someone I was traveling with had a couple guys on a motorbike pass by and grab her shoulder bag, pulling her down and dragging her for a while, during an initial walk after checking in at their hotel. No real harm done, and not too much stuff gone (a camera as I remember), but a heckuva welcome to Sicily! So be careful, and then enjoy!