No shuttle unfortunately. Great America and Levis stadium are both a in 10 minute walk. Peter's mention of BART or Cal-Train is your best bet for further travel. Lyft/Uber is fastest option, albeit most expensive.
No there is not a shuttle i used a cab but you can also take Bart
No. There's no shuttle from the airport. The best option is Uber/Lyft. If on a budget, catch the BART (train) to Millbrae station (1 stop), for less than $5, then get the CalTrain to San Jose/Diridon Station (about $7) which is only say 5-10 min easy walk from the hotel.
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