Wake up with the sun and wander through the cobblestone streets of Palma's Casco Antiguo, or Old Town. With the smell of café and tostadas lingering in the morning air, you'll purposely lose yourself between the Arab, Roman, and Catalan architecture encompassing your every step. In the area south-east of La Seu (Palma's tremendous cathedral announcing Palma Bay to all new visitors), you can find clusters of orange trees hidden within tiny gardens that aren't even on your city map. Touch the stone walls and feel the centuries of history which surround you. Look hard enough and you'll find at least one Miró which goes completely unnoticed by the untrained eye.
If walking isn't your strong suit, creep toward La Seu and find a horse and buggy which will take you on a sightseeing tour of the Old Town. A great photo opportunity which will show you some of the best conserved Mallorcan plazas. When you've finished, stop off near the Ayuntamiento (Town Hall) and get one last photo with the large, twisted olive tree in the Plaza del Cort. Head downhill until you arrive at Paseo del Borne, where you can browse and shop at some of the ritziest stores in Europe. If you're looking for a relatively cheap way to take it all in without the excess, walk into Casal Solleric between Zara and H&M and browse around this free art museum which has great rotating exhibitions monthly. Top it off by finally giving into your temptation and take a seat at one of the few tables outside the café next door. A more expensive espresso than other places, but when you check out the antique Italian machine they're using, you'll be convinced it's worth the price. Finish up your morning by crossing the Paseo and sitting down at one of the dozens of tables outside of Bar Bosch. Order a caña and a llonguet, chit-chat amongst the international crowd, and observe the thousands of interesting people passing by.
Just one morning in the Casco Antiguo won't allow you to see everything, but it might give you just enough to fall in love with it.