Generally speaking, both options are correct and you can use any of them in any context. People will understand what you mean. There is, however, a subtle difference between both expressions, so delicate that most native speakers will say that there is no difference. But there is. "Me habría gustado ir" is the conditional form of the Indicative Mode, whereas "Me hubiera gustado ir" is the imperfect preterite form of the Subjunctive Mode. The different modes point out a different hue of hypothetical sense: On the one hand, when a sentence is expressed in Indicative Mode, the speaker is pointing out that there is a certain level of "reality" in what he or she is saying. In the example "Me habría gustado ir" there is little chance that if you had finished your work on time, you would have gone. On the other hand, when a sentence is expressed in the Subjunctive Mode, the speaker points out the complete unrealty of what he or she is saying. In the example "Me hubiera gustado ir" the chance of finishing on time simply did not exist in the real world. Hope this explanation helps. :)

"Me habría gustado ir" would be correct in this sense because you are expressing a wish to do something if conditions would have been different. "Me hubiera gustado ir" you are expressing a wish to do something, but other circumstances occurred to prevent it. (e.g. Me hubiera gustado ir, si me habrían avisado con tiempo) I hope this helps

Hi JAN-jin, Both are correct, and there is also a third option "Me hubiese gustado ir". In this case there is not difference between them because is a hypothetical sentence.