My mother loved fresh tomatoes from the garden, and always hated to see the first freeze come and end the tomato season. So she decided to try a method to save the green tomatoes until they ripened and most years we had red garden tomatoes for Thanksgiving and sometimes for Christmas.
Here is her "recipe" for Saving Green Tomatoes.
Inspect the green tomatoes for bruises, cracks or any damaged spots. If they are damaged, keep them out on the counter to see if they will ripen. Do NOT wash the ones you are going to store. If they have long stems, trim the stems down so they won't poke their neighbors in the box.
Carefully wrap each tomato completely in a piece of paper or newspaper to protect it and place into the box. You can place them very close together, just not tight. Try to keep one layer and not stack them as they may "squish" as they start to ripen. If you have just a few, you can use a shoebox or two to store them, but will need to check them at least twice a week.
Close the lid on the box and place in a cool, dark place. We used to place them under the kitchen sink where the space for the water pipes made that spot cool. You can store them in a basement or anywhere at a temperature (ideally) of 50-60°F. The advantage of keeping them close to or in the kitchen is that you will remember to check them and it isn't such a pain to go downstairs or wherever. :)
Once a week (or more often), pull out the boxes, unwrap each tomato in turn and if it is showing pink, take it and place it in the kitchen to ripen. If it is still green, rewrap it and put it back in the box. If it is showing any signs of damage, leakage or mold, remove it and either use it or toss it. Replace the box back in the cool dark place, and continue this checking each week until all the tomatoes are gone.
As I said, with gentle handling, cushioned wrapping, and cool, dark storage, you can keep green tomatoes for a long time, and enjoy red garden tomatoes, maybe even for Thanksgiving and Christmas.