The phrase “wish to” expresses a desire or longing to do something. A synonym for “wish to” could be “desire to”. “Desire to” also conveys a strong longing or aspiration to carry out a particular action. For example, “She desires to travel the world and experience different cultures.”
Another synonym is “hope to”. “Hope to” implies a sense of expectation and optimism about being able to do something. For instance, “He hopes to get a promotion at work this year.”
“yearn to” is also a good synonym. It suggests a deep and intense longing. For example, “They yearn to be reunited with their loved ones.”
All of these synonyms for “wish to” help to express different degrees and nuances of wanting or longing to do something.