Both of the two recommendations above are good. However, you will need a car for both of them. In fact, San Jose is very spread out and you will likely need a car to get to just above any destination.

The Tech Museum, however, is within walking distance of the CC; it is a hands-on science and technology-type museum. It also has an IMAX. Another pleasant diversion within walking distance is the SJ Museum of Art. It has quite a small collection but occasionally has interesting special exhibits (such as the surfing exhibit last year -- fun, fun, fun) and its small cafe is nice (especially if the weather is nice and you sit outside).

Further afield is the Intel Museum in Santa Clara (car necessary).

Truth be told, there is not all that much to do in SJ, alas.