Visitors to San Jose usually at first do not realize that the metropolitan San Jose area includes many cities.  Santa Clara county (where S.J. is located) is made up of 15 incorporated cities/towns(Milpitas, San Jose, Morgan Hill, Gilroy, Campbell, Los Gatos, Saratoga, Monte Sereno, Santa Clara, Sunnyvale, Cupertino, Los Altos, Los Altos Hills, Mountain View, and Palo Alto) There are also many unincorporated areas within the county (even completely surrounded by a city in some cases)  that fall under county jurisdiction.  

San Jose itself has many neighborhoods/districts. They include Willow Glen, Almaden, Cambrian, Evergreen,  Blossom Valley , the Rose Garden, Alum Rock, West San Jose, East side, Winchester and Alviso. 

It is also worth noting adjacent counties:  Alameda (Fremont, Oakland, etc), San Mateo (Woodside, Menlo Park, Redwood City, SFO, etc), Santa Cruz (Boulder Creek, Scotts Valley, etc).  The entire San Francisco Bay Area metropolitan area is mostly one continuous meld of population and urban development.