At the top of my list is anything that is either too expensive at the grocery store (esp. $2.00+/lb; we don't live in an area w/cheap produce!), or is not readily (or at all) available. Fresh herbs, tomatoes, peppers, eggplant, shallots are at the top of the list. Fruits too, which for us include berries, pomegranates, paw paws, figs, quince, lemons, oranges, persimmon, guava, kiwi, and I forget what all else...
Then there are the things that are FUN to grow, like melons, corn, potatoes, sweet potatoes, garlic, onions, peas, beans... The list could go on and on. I would definitely have detailed conversations with your local extension office. We moved from the Pacific NW to coastal Georgia and were quite flummoxed by the very different gardening rhythms. It's taken us a while to get the hang of it, and the extension office knows us well now. :)