Though, if they searched them as well as they searched the rest of the park, I can't say I have much confidence in how thourough a search it was.
My thought is that Chandra was killed at the park, but not out in the open. Condit couldn't risk having her meet him anywhere anyone would recognize him. That's why she was researching the park and Klingle Mansion on her computer. He told her where they would meet. She was unfamiliar with the location.
As it turns out, the mansion was closed to the public that day. How convenient.
Now we also know that Condit liked to ride his bike to the park, so he would be very familiar with the accommodations.
The only problem with this is how to dispose of the body. It would have to be kept out of sight until it was safe to move it, probably after dark. An outbuilding or garage would work nicely, or the trunk of a car. The body would have been in its final resting place long before any search occurred.