Which "LA" team??? The Los Angeles Dodgers, which is near the Downtown LA/Hollywood area, or the Los Angeles Angels of Anaheim, which is near Disneyland.
If you are planning to see an Angels game, then stay in the Anaheim/Garden Grove area, plenty of access to Shopping and many other places, head to the Anaheim Forum and check out the Top Questions that talk about Public Transit.
If you really want to go to Tijuana by yourself, take the Amtrak Pacific Surfliner Train south to the last stop, the Santa Fe Station in Downtown San Diego, and transfer to the San Diego Trolley Light Rail System to San Ysidro and cross the border. Just plan ahead, to cross back into the US, you can find waits up to 2 hours to go through Customs and Immigration.
If you are head to a day game at Dodgers Stadium, I would still stay in Anaheim, and take the Amtrak or Metrolink train to Union Station (North) and catch the Dodgers Express.
Alas, the last Amtrak train southbound leaves Union Station around 10 PM, so not practical for a night game, so I would look at the Hollywood and Highland area for a Hotel room for that night at least.