San Jose’s downtown and central areas (close, but not quite in downtown) encompass a large area with many distinct neighborhoods.
Within downtown San Jose you’ll find Naglee Park, Japantown, Vendome, and many other residential areas near parks, schools, transit, or businesses & shops, many of them historic and with gorgeous architecture. Of special interest is the access to light rail, CalTrain, and BART in these areas (BART is making its way to the Diridon Station in downtown San Jose in the coming years).
If you love newer construction and a low maintenance lifestyle, you should know about the Altura neighborhood, which is in San Jose but right on the Santa Clara border (and close to the Santa Clara train station).
Some Santa Clara neighborhoods, such as University Square, are just beyond the Central San Jose area and for those spending a lot of time in downtown, this is an area worth considering, too.