I feel like the easiest way to get from Santana Row to the SAP Center is just to take San Carlos/Stevens Creek about a mile east, then turn north up one of the side streets. Either that or take 280 to 87 for a very short distance.
While you can fly directly into San Jose, check the prices for San Francisco and Oakland - they're not far and maybe you'll save some money.
I could recommend the Rosicrucian Egyptian Museum - it's about a mile west of the SAP Center. The Tech Museum is well known - I haven't been since I was a teenager, and I believe it's pretty expensive, but may be worth it. If you're a reader, there is a rather large used bookstore (Recycle Bookstore) about half a mile west. I frequent it regularly when I'm in San Jose. This is all in San Jose itself.
Further afield, if you're interested in gardens or architecture, there is an old mansion named Filoli about half an hour north of San Jose on Highway 280. There are also tours available at the Stanford Linear Accelerator Center. The Lick Observatory is about an hour away, on top of Mt. Hamilton.
I live in the Monterey Bay area, so I'm not as familiar with San Jose and the San Francisco Bay Area (even though I actually went to San Jose State), but I can highly recommend visiting the Monterey Bay - either in the Santa Cruz area (easily accessible via Highway 17, with bus access) or further south in the Monterey area (about an hour's drive - you can take the bus there but it's not very convenient).
Santa Cruz has great beaches, the Santa Cruz Beach Boardwalk amusement park, plenty of unique local shops and artists, and plenty of outdoor parks (I can recommend the UCSC arboretum as well).
Monterey has great beaches and parks as well, the famous Monterey Bay Aquarium (although no whales), lots of local historical sites (Monterey is a former capital of California), some shopping, and tons of golf courses. If you are ambitious, you could even go as far south as Big Sur along the magnificent coastal highway.