There are two ways to open a cryptex - the way it is meant to be opened, with the combination, or by bypassing it in some way. It's quite easy to get inside without the combination - the hard bit is doing so in such a way so as not to release the acid and destroy the document inside.
If the PCs want to try the second method, I would ask for a DC 30 thieves tools check. If they fail by 5 or more the acid breaks. Otherwise they can try again.
If they want to try guessing the combination, you need to decide if the character's have a better chance of guessing than the players. You might just pick a password and let the players guess. If there is some reason why the character might have a better chance of guessing - e.g. it's the name of the First Emperor of Puzzleopolis, you might allow an appropriate skill check - history in this instance. But if it's just a matter of blind guessing, then no amount of Investigation skill is going to help.
I guess another way would be to blindfold a halfling and let them punch keys randomly. If they roll a 1 on the D20 the lucky trait triggers and it opens.
Divination magic might also be used.
You might allow them to try and look for fingerprints on the keys - don't prompt the players, they need to come up with this on their own. In which case a DC 15 Investigation check gives them an anagram of the password.