I believe that is septoria, a fungal disease that tomatoes are very prone to (mine almost always get it before the end of the season).
Start by removing and trashing all the diseased leaves (not in compost pile). Be sure your garden beds are well mulched to help prevent soil from splashing up onto the plant. Remove all the lowest leaves and be sure nothing is touching the soil. Only water the soil, not the plant/ leaves.
Neem oil is anti-fungal. I haven't used it. Other organic treatments include: hydrogen peroxide (sprayed straight from the bottle, which is 3% concentration), baking soda solution, diluted milk. You can only use one at a time, but you can rotate them, since your plant should be thoroughly sprayed (including undersides of leaves) every week or so. All the fungicides (including the bad chemical ones) work better preventively than trying to treat established disease.