Hello, TXtrish, and welcome to the Visalia forum.
Lots of chains in Visalia for breakfast, including Hometown Buffet, but that's not what you are looking for. Here in the San Joaquin Valley, there *are* some mom and pop type places that serve breakfast, though I'm not aware of anything to suggest in Visalia itself that meets your criteria.
Try The Green Valley Cafe in Hanford, just about that proverbial 15 - 20 miles away to the west on California State Route 198. Exit 10th Avenue and head north to the restaurant at 740 North 10th Avenue in Hanford, in the NE part of Hanford closest to Visalia. (559) 583-1831 is the telephone for them. Lots of huge pancakes, omelettes, chicken fried steak, and biscuits and gravy. Very generous portions in my experience. Beats the chains hands down. Check 'em out!
If you are able to have a meal at 11:00 AM or later, Superior Dairy Products, 325 North Douty Street in downtown Hanford is the spot for ice cream and sandwiches. . . emphasis on the fresh ice cream. Fifties style diner and experience.
Enjoy your travels with us.