What is a place of articulation which best fits the initial consonant of the word travel? It looks like the first sound is /t/ therefore it should be alveolar, but in the Longman pronunciation coach (Exercise 3) it's marked as post-alveolar. Why so?
A canonical /t/ is indeed alveolar. However, when a /t/ precedes an /r/, the /t/ moves back in anticipation of the /r/, which has a post-alveolar articulation. When this happens, the articulation of these two sounds together forms a new sound, an affricate (called a "post-alveolar apico affricate"!). This sound is very similar to the realisation of /tʃ/ which we find in church, referred to in schools as the 'ch' sound. Whether the 'tr' sound actually is in fact the same sound as the 'ch' sound is the subject of much debate.
So, if you are a non-native speaker aiming to pronounce "travel" like a native speaker, you are best off aiming for this pronunciation:
You won't find this transcription in a dictionary, but it best describes the actual sound we make.
In American English, after obstruent [t] or [d], an [r] assimilates to become an obstruent also. (An obstruent is a consonant which obstructs the flow of air enough to make it naturally voiceless, though it may still be voiced.) Since the [r] is a palato-alveolar, rounded, and retroflexed liquid, after [t] or [d], it becomes a palato-alveolar, rounded, and retroflexed obstruent. This is what you get in a word like "dream". After [t], furthermore, it assimilates in voicing to become voiceless. It's a rather odd sound -- there isn't any good phonetic symbol for it.
I think "post-alveolar" means the same as the term "palato-alveolar" which I used above. Sometimes this is called "alveo-palatal".
It would be perfectly plausible for the [t] preceding this palato-alveolar to then assimilate in position and change from an alveolar position to become palato-alveolar also, and I suppose the Longman's account reflects this change. Personally, though, I find this further change does not happen in my own speech (I'm from Ohio, originally), and the [t] remains alveolar in position. However, the following sound causes it to become laminal, meaning that the blade of the tongue is the articulator, rather than the tip of the tongue.
Evidently in the local dialect of English here in Hawaii, this further change of [t] to palato-alveolar does take place, since it changes a preceding [s] to become palato-alveolar also, in words like "street".