One thing you can do is get a vacuum sealer and cut up and seal some tomatoes till you have enough for a batch. They won't keep like canned tomatoes, but they will keep for a week or more better than just on the counter top.
I'm going to ask for a vacuum sealer for Christmas to use for next year because I'd like to freeze some berries too and of course tomatoes, and other veggies from the garden that I don't like the taste of then they get canned.