Princess Leia's "Help me, Obi-Wan Kenobi. You're my only hope" is one of the most iconic lines from Star Wars: A New Hope, but some may question why the Rebellion was so intent on finding Obi-Wan Kenobi specifically, especially since Yoda was still alive at the time. While a meta answer to the question of why Leia was searching for Obi-Wan might just be that Yoda's character was not finalized when Star Wars: A New Hope was filmed, the in-canon answer is not readily apparent in the original trilogy. However, supplemental content reveals more about why Obi-Wan was the Rebellion's first choice of Jedi.
At the end of Star Wars: Revenge of the Sith, Bail Organa, Obi-Wan Kenobi and Yoda sit down to discuss the fate of Luke and Leia. In this meeting, Bail Organa agrees to adopt Leia, and Obi-Wan brings Luke to the Lars family on Tatooine where he watches over him. Yoda, for his part, keeps silent about his own plans for the future, stating, "Until the time is right, disappear we will." With this vague pronouncement, which may have some relationship to his Force vision ability, Yoda effectively cuts himself out of future plans to fight against the Empire until he deems it necessary to return.
Whether or not this was the right choice for Yoda is up for debate. He might have been able to continue to help the rebellion, either by joining the Rebel Alliance's leadership or working in secret to rebuild the Jedi Order. The decision to go into hiding also contrasts sharply with his role in the new Star Wars: The High Republic subseries, which shows that in his younger years, Yoda was a far more active and confident player in galactic affairs and Padawan training than his choice of exile suggests.
Because of Yoda's self imposed exile, at the beginning of Star Wars: A New Hope, he is unknown to most of the Rebellion. For example, Luke was completely unaware of Yoda's existence until Star Wars: The Empire Strikes Back. On Hoth, as Luke is on the verge of death from a combination of the wampa attack and hypothermia, Obi-Wan appears as a Force ghost and urges Luke to seek out Yoda in the Dagobah system. This scene shows that Obi-Wan, at least, knew Yoda's location. Luke's confusion also proves that most of the rest of the leadership of the Rebel Alliance was unaware of Yoda's survival. Otherwise, at least one person might have mentioned to Luke that there was another Jedi master out there, even if Yoda was nowhere to be found.
Therefore, Obi-Wan was the main Jedi that the Rebellion could seek out to help in the fight against the Empire, and by the time of Rogue One: A Star Wars Story, gaining Jedi aid was one of the Rebellion's top priorities. In that film, Jyn Erso and her team got the plans for the Death Star and sent them to Leia's ship, the Tantive IV. However, as revealed by 2015's Star Wars: Absolutely Everything You Need to Know, Leia's trip to Scarif was a detour. Originally, Leia was heading to Tatooine to find Obi-Wan, but the Death Star plans became a higher priority, necessitating Admiral Raddus chart a course for Scarif to help.
Bail Organa might have had other motives for assigning Leia this mission. As Star Wars: A New Hope may hint, Leia may have begun showing Force sensitivity, and Bail might have intended for Obi-Wan to confirm her Force ability. Bail also might have suspected that Obi-Wan knew Yoda's location, and therefore searching for Obi-Wan might have been the first step in a search for Yoda as well.
Thus, Leia sought out Obi-Wan instead of Yoda because Obi-Wan was the only Jedi easily available for the job. Still, the movies and new canon materials provide more reasons why Obi-Wan was the better choice of Jedi for Leia and the Rebel Alliance to seek out in its darkest hour.