How do they call a trip that you sleep in one place and each day you go to another direction? Is there a name or a slang for this? I want to search for information about that kind of trip and I don't know what should I write in the search engine. (in Hebrew we call it a 'star trip')
It sounds like you're looking to do a series of day trips [TFD]
a journey made to and from a place within one day
At the end of each day, you'd return to your chosen home base [MWD] (not necessarily your home)
the place in which someone or something lives or operates
For examples, you could google "day trips in your destination"