The Bible says nothing at all about pilgrimages. Pilgrimages are a feature of false religions and come from the practice of idolatry.
The closest the Bible comes to pilgrimages are the various feasts under the law of Moses which were celebrated at the Temple in Jerusalem. Since the end of the law which was fulfilled by Christ and the destruction of the temple by the Romans around AD 70, even these events which, in a stretch, could be called pilgrimages are no more.
I hope you have found this helpful.