The only caves with limestone formations that I know of are in the Sierras or the Cascades. These are in the Gold Country around Sonora and Angels Camp. There's also Boyden Caverns in Kings Canyon, which has a little stream running through it. There are some by Mt. Shasta and Lava Beds National Monument. Shasta Caverns is up by Lake Shasta.
Farther north is Oregon caves.
The Bear Valley Cave is huge and has a creek flowing through it.