Answer: Although the damage appears to be insect related, I think what you are dealing with is most likely blossom end rot. It is relatively common and caused by a lack of calcium to the tip of the fruit. When the cells in tip of the tomato lack calcium during growth, they die and the black decay you see follows. You may have adequate calcium in the soil but still get blossom end rot due to soil moisture fluctuations (from wet to dry). I have noticed that blossom end rot is worse on the first tomatoes of the season and tends to not affect later fruit as much. Blossom end rot is best prevented by keeping the soil evenly moist. Garden centers sell a spray which contains calcium and can be used to prevent blossom end rot. This must be applied starting when tomatoes are about marble sized. Mulching will also help keep soil moisture even.
Toss the affected tomatoes and keep the soil consistently moist and I think you'll see an improvement. Best wishes with your tomatoes!
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