1. The shuttle itself - this needed extensive maintenance work done to it after each flight.
2. The big orange fuel tank - this couldn't be reused
3. The solid rocket boosters on either side - these had to be completely rebuilt after they splashed down in the ocean (it is easier to splash them down in the ocean than the Falcon 9 first stage, as they separate at a lover altitude).
Overall this didn't save much on costs, with the average cost of a flight (inclusive of development costs) being about US$1.5 billion.
Including complete rebuilds for the three Space Shuttle Main Engines (SSMEs), they were I gather somewhat needlessly too high performance/sports car types of devices.
In general, the Space Shuttle design was twisted by various unnecessary requirements (e.g. while the Air Force didn't want it, it could originally do a single polar orbit mission, which required extreme heat shield technology to land back at the same location while the earth turned underneath it. This was later mitigated by replacing a lot of those tiles with a ... glass fiber mat???), and to minimize development costs. Solid fuel booster you can't turn off were formerly considered to be unacceptably dangerous for manned missions, but they were the cheapest to develop.
Operating costs? Well, NASA post-Apollo makes the most sense if you view it as a public works project.... Low launch rates, especially post-Challenger after more people realized what an abomination it was, plus a huge fixed work force made it very expensive to operate.