Alhambra is intersected by the east/west Interstate 10 with exits at Fremont Ave, Atlantic Blvd, and Garfield Ave, the main north/south arteries of the city.
Alhambra is accessible by LA Metro Bus routes 76 (Main St) and 78 (Valley Blvd). Detailed routes and schedules are located at the LA Metro  website.
Alhambra is a walkable city in some areas (Main St, Valley Blvd) but you are likely to want to rent a car to see the surrounding areas as well. The bus is a cheaper, but slower option.