Broccoli is a good companion to dill.
MEDITERRANEAN gardeners have always put basil and tomatoes together in the kitchen as well as in the garden. Many people believe that the odors from the aromatic oils produced in basil leaves help to repel insects that might otherwise bother the tomato plants. This may or may not be so, but planting them near each other is definitely a good way to combine two tasty crops.
When it comes to the science of companion planting, it is difficult to prove any definite cause and effect relationships. Life in the garden is a little different every year, so it is almost impossible to replicate the exact growing conditions from one year to the next. One thing is certain: you should organize the vegetables in your beds to avoid competition for space and sunlight.
Early in the growing season, tomato plants are small and don't create much shade; radishes or lettuce can be grown nearby and will be harvested before the tomatoes reach maturity. Late in the season, tomatoes will shade nearby plants and may sprawl over them if they're not supported by ladders or cages. Lettuce and other leafy greens (such as basil) can tolerate some afternoon shade, so they will do fine near tomato plants. Peppers and eggplants, on the other hand, need full sun all summer long and should not be overshadowed by neighboring plants.
Marigolds, garlic and onions are thought by some to repel pests. There certainly is no harm in growing these plants in several locations in the garden. Radishes tend to attract flea beetles, so some people plant them near broccoli, eggplants and turnips as a trap crop (flea beetles may eat the radish leaves in preference to the crop you are trying to protect). An alternative, of course, is to cover your eggplants or other plants with garden fabric (row covers) to keep the pests off the plants.
You may want to give a few of the most commonly-recommended plant companions a try and see if you notice a difference in health or vigor. Keep good records and eventually you may feel like you can make some definitive recommendations.
Here are a few traditional groupings to try:
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