Not unripe tomatoes, but tomatoes that are still green when they are ripe? All of these can be grown from seed in your garden. How are they different in taste? You'll have to grow some to find out. Seed companies have dozens of different kinds of tomatoes to choose. For example, Baker Creek Heirloom Seeds has seeds for 141 different types of tomatoes.
The same principle applies to other vegetables. Baker Creek has 24 varieties of summer squash, and 80 kinds of winter squash. They have 53 varieties of watermelon, and over 79 types of other melons. These are seeds that they have collected from all over the world, so you can sample some of the foods of other lands, without ever leaving your own garden.
More exotic seeds are also available. Perhaps you'd like to try growing narajilla, a sweet and sour fruit from the Andes mountains, the juice of which has been described as the nectar of the gods. Or Thai mung beans, which have a nutty taste, and are used in Thailand for making deserts.
Believe it or not, it is even possible to get seeds for some rare tropical fruits. Of course, whether you can make them grow depends on the climate where you live. However, even if you're not up to the challenge, Trade Winds Fruit is an enjoyable site to browse though. You'll be amazed by what you're missing.
Seedman is another nice site for seeds from all over the world. They too have seeds for tropical fruit and nut trees, as well as seeds for exotic vegetables, herbs, flowers, cacti, etc. Something especially interesting on their site is the section for cold hardy palms, banana, yucca, and cycad seeds.