I haven't been to the Tech Museum myself, but my dad went a few years ago and said it was pretty boring. The IMAX movie you get with the ticket was nice, but the museum itself was boring.
The Winchester Mystery House is pretty sweet, and you can get pretty close to it on the 23 bus from downtown. It's right across the street from Santana Row which is the real expensive shopping center.
Otherwise I would take Caltrain up to SF. Either take Caltrain to the end of the line and then take Muni light rail where you need to go, or take Caltrain to Millbrae and transfer to BART. In SF I would suggest checking out Coit Tower, Cable Car Museum, and Chinatown (if you like trinket shopping and food). If you've never seen the Golden Gate Bridge you can probably find a Muni bus that will take you from the financial district (where the BART stops are) to the bridge.
If you're going all the way to the financial district I believe cheapest way is to take Caltrain to the end of the line and then get on the Muni light rail that is across the street from the Caltrain station. Also if you leave San Jose early enough in the morning you can get an express Caltrain it will save 30 mins over the local service ones. Same thing with coming back in the afternoon.