I think the Caves of Drach are excellent Barb, however, they are a fair way away from Palma and I'm not sure you should commit to that, seeing as you aren't on the Island for that long a time. It will probably eat up three quarters of a day either on a dedicated trip or by public transport.
The open top bus is a great way to see Palma as well. I think walking around the cathedral and surrounding streets will give you your fill of architecture for the trip. It's a big City and you could do more than one day there.
If you are there on a Wednesday, you could take the bus to Andratx (Town) as there is a huge market there on Wednesdays, it's not all tourist tat, sights sounds smells colours all come alive with this trip. You could also walk around the (public, free entry) Cactus Gardens in town, they are well maintained and a good relaxing half hour.
There's lots to do in Mallorca (vineyard tours around the town of Binnissalem are also good), but you are a little more limited without a car.
You'll have a great time anyway