How many weeks before a growing area's last frost date should tomato seeds be started indoors?

That depends on several factors. Will you be using bottom heat, which helps seedlings off to a faster start? Will you be using grow lights? Or will you use a sunny Windowsill or glassed in warm porch?

Let's say your last frost date is May 15. Your goal is to have tomato seedlings ready to go into the garden two weeks after that, when the soil has warmed up a bit. You also want your seedlings to have a small rosette of leaves atop a large root ball. You achieve this by planting three seeds in each of several small paper cups with holes punched in the bottom for drainage. Two or three weeks later, select the strongest seedling and snip off the other two, leaving just one. Snip off this strong seedlings' lower leaves, and plant the root and leafless stem in a larger paper cup with drainage holes to within a half inch of the top rosette of leaves. Three transplantings into larger paper cups each time results in roots forming all along the buried stems, giving you a large root ball and small top, just the opposite of the spindly seedlings for sale at the nursery.

If you're using bottom heat and grow lights, transplant every two weeks, so you'd start your seedlings four or five weeks before the last frost date. If you have only natural sunlight, give yourself six weeks before the last frost date to make the three transplantings. Remember to plant into the garden two weeks after the last frost date. Tomatoes planted into cold soil will sit there and sulk. They'll be more prone to fungus. And their growth will be set back. It's much better if these sun and heat-loving plants are put into warm garden soil.