One of the first students to be sent away for education may have been the son of José de la Guerra y Noriega, Juan José Noriega, who was sent to Liverpool, England for education in 1825. When he returned to California in c.1831 at the age of about 21 he was tutored in higher mathematics by Father Patrick Short who in 1834 jointly with William Hartnell, who had engaged him as Noriega's tutor, founded the first school/college in California. Noriega died in 1833 but in a way his legacy, the relationship between Hartnell and Short, led directly to the foundation of the "Colegio de San Jose".
The explanation for this theory involves William Hartnell, mentioned in this question and also in the following question which provides some of his background:
Who was the first retailer in Monterey, California?
Hartnell had a business associate in Liverpool called James Brotherston who was the co-partner of John Begg of Lima who was the co-partner of McCulloch Hartnell & Co. Brotherston appears to have had the senior role, and referred to McCulloch Hartnell & Co as the "California Establishment". He was by the way John Begg's brother-in-law, being married to his sister, which seems to have been how the business connection started (in Leith, the port of Edinburgh, Scotland). I digress!
It is clear from letters that Brotherston wrote to Hartnell on 7th October 1825 and 20th January 1826 that Hartnell had sent his (then future) brother-in-law Juan Jose Noriega to the care of Brotherston in Liverpool for his "improvement and education". In the first letter Brotherston states his plans for the boy's education including the subjects he will study and the likely costs. The second letter just gives a brief progress report towards the end of a business letter. The following are links to the actual letters in the Vallejo volumes:
Then on 19th March 1827 Juan José Noriega himself wrote to Hartnell from Liverpool and lists the subjects he is studying but doesn't say much else except that he's too busy to write to his sister!
On the 29th October 1828 he writes a longer letter to Hartnell from Stonyhurst College in which he says he has been at three different schools, the previous ones being in Liverpool and Shropshire. It is apparent from this letter that he is becoming homesick for California and talks about his plans for returning there, preferably avoiding Cape Horn.
Bancroft in his "History of California:1825-1840" refers to the above letter and states that he was later educated at the "Mont." school under Hartnell and P.Short. He includes the information that Noriega died in 1833 unmarried. In fact Bancroft is incorrect as the school was not formally founded until 1834, after Noriega's death.
Chapter 5 - 'Schoolmaster' of Dakin's "The Lives of William Hartnell" explains in detail the events surrounding the return of Noriega, the engagement of Father Patrick Short as his tutor, and the subsequent founding of the "Colegio de San Jose".