One of the easiest ways to "see Palma in a day" is by the Number 50 sightseeing bus (approximately every 20 minutes) which takes in all the major sights of the city.
Like most City Tour buses, you can hop on and off the bus at any point, and tickets are valid for a 24 hour period. The total journey time for the round trip is 1 hour 20 minutes.
The service starts at 10am and operates until 10pm in summer, 8pm in spring and autumn and 6pm during the winter months. There are personal headphones available and a guided commentary in 8 different languages.
Take a look at this website for the start point, tour costs and map of the route (insert Palma de Mallorca in the box on the left top of the page):