Luckily for you, San Jose is chock full of mom and pop eateries. As a San Jose native and a professional Chef, I've eaten at alot of places in San Jose, some good, some bad. Here are my suggestions:
*Mexican: Honest to God, I swear by this place as I have been going there since junior high and it is as authentic as it gets, despite the name: The Burrito Factory on Almaden Expressway. Their telephone number is: 408.448-7180. Do NOT confuse them with the Burrito Factory on Blossom Hill Rd. which has the same name, polar opposite food.
*Japanese: Try Kazoo in Japantown. Their number is: 408.288.9611. They are located on Jackson St. There is also a Japanese grocery store across the street in case you wanna pick up some snacks or a bottle of Sake. Stay away from Todai though! There is nothing authentic about it, its located in a mall, and in a way its like a huge, Japanese style Panda Express, but with cartoon pufferfish and cute to go cups.
*Local foods and meats (probably not so hard to come across in CA): Three Words: Sonoma Chicken Coop. They are located downtown on Market St. Their telephone number is:408.287.4098.
*"Authentic ethnic": Hmmm, well, that could be anything! My fave: Zeni Ethiopian Restaurant on Saratoga Ave. The portions are large, cheap and freakin' amazing! Their number is: 408.615.8282. For Thai, try Blue Mango on Stevens Creek Blvd. I dig the Pad Thai myself. Their number is: 408.248.7191
*Fine wine, whisky, and beer: My all time fave downtown "Americana" hot spot is the Tied House. Good food, house brewed beer, cool ambiance, and a pleasant staff. Their number is: 408.295.2739
I hope this helps! Enjoy your stay in San Jose and dont drink and drive in Downtown on Friday and Saturday night, the cops will get ya'!