The previous posters have some great suggestions...
I also would highly recommend the Winchester Mystery House (525 S Winchester Blvd) and Santana Row (located directly across the street).
HP Pavilion (525 W Santa Clara St) also hosts the San Jose Stealth (a professional indoor lacrosse team). The San Jose Sharks are currently fighting for a playoff spot, so a hockey game in the next month or two would be fun.
The Tech Museum (201 S Market St), I agree, is just OK, but it does have an IMAX theatre which does show newly released movies from time to time.
If you are into art, you can also go to the San Jose Museum of Art (111 S. Market St). Admission is free.
If you are into historic churches, there is the Cathedral Basilica of St. Joseph (located right across the street from the San Jose Museum of Art at 80 S Market St). Also, Mission Santa Clara is not too far away, on the Santa Clara University campus (500 El Camion Real, Santa Clara).
Lick Observatory is also in San Jose (albeit a 1-2 hour drive from downtown San Jose @ 7299 Mount Hamilton Rd) - it is home to what once was the largest telescope in the world.
If you are looking for amusement parks, Paramount's Great America is located in neighboring Santa Clara (1 Great America Pkwy, Santa Clara, CA), and there is a waterslide park called "Raging Waters" within the city limits (2333 S White Rd).
There's also the Center for Performing Arts (255 Almaden Blvd) which is currently hosting "The Lion King."