What good resources are available to assist first-time travellers to learn basic Chinese?
I would suggest a short intensive course in Chinese done through Comprehensible Input (that's a theoretical framework for language acquisition). You can also search for TPRS-based courses or teachers of Chinese -- that's the name of the language teaching method that uses this approach. Problem is, there aren't that many out there yet.

The problem with a phrasebook is that it's just that -- a book of phrases. It doesn't build the ability to understand or create with the language. Doing a CI-based course, even a very short one, will give your visitors a lot more flexibility with the language. I've had people go to China after 8-10 hours and get along quite comfortably (able to buy things, eat, talk about themselves, and so on.) They're not going to be UN interpreters the next day but this kind of preparation goes a lot farther than memorization.

Traditional lessons or textbooks also fall short for short-term classes because they are not really much different from a phrase book. The student focuses on one "pattern" or a dialogue for a couple of hours, and doesn't develop much ability to use the language within the time they would have to devote to Chinese study before their trip.

In the US, Albany Language Learning or Fluency Fast do this sort of course. These are both Western-student-oriented organizations in the US, and will focus on the highest-frequency words and structures in the language. Full disclosure: I work for Albany Language Learning. But if I knew more sources I'd point you to them. People just get a lot farther in a shorter time when preparing for travel in this way.