Fishing is real crummy right now. Cold. As already mentioned, Calero from shore is a good way to get bit and catch some fish. Calero has nice quality, like a good bunch of 3-5lbers. You could drive 50 minutes south to Coyote and shore fish there but bring your mud boots, it's super low and muddy. It's the kind of thing if you went right now you would probably get 1 or 0 bites but if you got 1 bite it would be a nice fish.

Steven's Creek, or Lexington (muddy) are close by. Steven's creek is brutal for bass fishing. Lexington you can get bit on decent quality like Calero but the mud may be crazy bad right now, like up to your knees.

There are a few small ponds you could google for that are closer to San Jose like the Campbell perc ponds or Almaden. I don't know much about those, but they're close by and I think they are free to fish.