Minimum size kayak = what you are safe and comfortable being out in the elements in. I would recommend a 12' minimum, but again, personal comfort level.
Set your expectations appropriately. Bluefin Tuna is incredibly unlikely, and yellowtail are challenging. You might catch one on your first trip, you might still be hunting 10 trips in.
Kayak transport would be Avalon Freight Services - rate as of 5 years ago was ~$35 each way, but you'd want to check in with them for current costs.
But "for a day" will be challenging. Their boat leaves at 4pm in the afternoon, so you'd need to drive up the day before, leave your yak with them, stay locally (or make the haul back down the coast), then catch the ferry across, pick up your yak, try to fish for a bit, then get it back to the freight company in time to do paperwork and not miss your ferry back, then hang out and wait for your yak to make it back that night/next morning.
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