From the Super Mario Wiki
Star Hill is the name of a mystical hill in the Mario series. While its appearance has changed in each appearance so far, it is usually lauded for its beautiful and romantic view (Mario is even advised by a Toad to take Princess Peach there on a date). Star Hill is literally seen as the place where wishes come true.
Super Mario RPG: Legend of the Seven Stars
In its debut in Super Mario RPG: Legend of the Seven Stars, Star Hill is located in the southwest region of Mario World, and is made out of many smaller hills which look like dark blue meteorites. Mario, Mallow and Geno travel here for one of the seven Star Pieces. This Star Piece is the only one that can be taken without a fight; it rests on the ground at the end of Star Hill, unguarded by anyone (most likely because the player fought in Booster's Tower and Marrymore).
It is impossible to traverse the entire hill simply by walking; the only way to access different areas is by lighting several of the unusual star-shaped flowers, causing a keyhole in a large star in the area to grow. Going through the enlarged keyhole allows the enterer to travel to another area instantly, and the keyhole shrinks behind them. The hopeful fallen stars that litter the area can be examined to hear the wishes of the people who made them. Two of these wishes will come true over the course of the game, and if the wishes are examined after it comes true, the wish will be changed. Reading Mallow's wish will cause him to lash out at the player in embarrassment, and reading his parents' wish will make him mellow.
In Paper Mario, Star Hill is instead directly north of Peach's Castle, although it is renamed Shooting Star Summit in the English version. Unlike its previous appearance, the stars the mountain is famous for cannot be interacted with, and are seen to be shooting stars of various colors that constantly scatter and fall harmlessly on its grounds. At the base of the hill lies Merluvlee and Merlow's house, where Mario can have his fortune told and trade Star Pieces for badges.
During the events of the storyline, Eldstar notifies Mario in a dream to head to the summit for counsel after Bowser takes Peach's castle to the sky and easily KOs Mario. Once he has awakened from his unconscious state after many days and Goombario's family revives him, he heads to the summit. Once he arrives, all seven Star Spirits appear (using the last of their power to create a projection) and reveal to Mario he must rescue all of them to save Princess Peach. On his way back down the mountain, Mario is introduced to Twink, who gives him the Lucky Star from Peach and teaches him how to use the Action Command. A Magikoopa then appears, having followed Twink to Mario, and must be defeated. Once the Star Spirits are physically gathered together later on, they use their power to open the Star Way, a celestial trail which leads to Star Haven above.
Mario & Luigi: Partners in Time
In Mario & Luigi: Partners in Time, Star Hill is again shown to be north of Peach's Castle. It is only explored in the past, where it appears to be made of glittering stars and contains Star Shrine accessed at the top.
Star Hill is quite a small area, and enemies include Love Bubbles, Handfakes and Fly Guys. The "spirit of the Cobalt Star" (in reality, Elder Princess Shroob) speaks to the Mario brothers and their younger selves on top of the hill after Commander Shroob is battled and defeated there. A pipe to Star Hill can be found in the destroyed Toad Town near the Time Hole to the basement of Peach's Castle.
Names in other languages