APRIL 10th1854.—Oakland, on the eastern side of the bay directly opposite San Francisco, is to the latter, something like what Brooklyn is to New York. Between the two former places there are frequent daily opportunities of communication by steamers. Many people who carry on business during the day in San Francisco, have their dwellings and families at Oakland. The latter is one of the sweetest and most beautiful places on the bay. It is a great excursion quarter for holiday folk from San Francisco. As its name implies, Oakland is celebrated for its trees, of the live-oak kind, which give at all times a peculiarly cheerful and refreshing character to the place. Recently a small village, then a thriving town, it has now assumed the name, if not all the pretensions of a city, although the inhabitants number only two or three thousand. Of this date, the first election under the city charter took place, when Mr. Horace W. Carpentier was chosen mayor.