We report a study of the CHA-type aluminophosphate AlPO-34, prepared with six different structure-directing agents (SDAs): piperidine (pip), morpholine (mor), pyridine (pyr), 1,4,8,11-tetraazacyclotetradecane (cyclam), 1,3 dimethylimidazolium (dmim) chloride and 1-ethyl-3-methylimidazolium (emim) bromide. Using a combination of solid-state NMR spectroscopy, periodic density functional theory (DFT) calculations and synchrotron X-ray diffraction, we show that, even in crystallographically well-ordered materials such as AlPO-34 with dmim as the SDA, local disorder may be present. For such disordered structures, where it is challenging to use DFT to assign NMR spectra, we show that the 31P isotropic chemical shift can be predicted accurately using the mean P-O bond length and P-O-Al bond angle, in an extension of previous work. Variable-temperature 27Al NMR reveals the presence of microsecond-timescale dynamics in all forms of AlPO- 34, with two different motional regimes observed, depending on whether structural H2O is also present. H2O is detected in AlPO-34 prepared with mor as the SDA, although this material was previously reported as anhydrous, suggesting that this form of AlPO-34 may be hygroscopic despite the presence of the SDAs within the pores.