You might try Shark Fin Melon greens (not the fruit). They grow fairly fast, and don't require as much light as most cucurbits. Just plant a bunch of seeds and let them go until they're big enough to eat, prune off what you want, and let them grow back. Don't eat the seed leaves (cotyledons), as they're bitter. A disadvantage is that they grow long vines (they're not bushy).
Grandpa's Home peppers are supposed to be good even as houseplants. They're said to be shade-tolerant. I'm growing some outdoors, now, in the shade. They're doing decently (but took a while to fruit). They look pretty nice with the fruit on them, too. I haven't tried them indoors, yet. Many other hot peppers can do well indoors.
Ground cherries are very workable in containers indoors. They'll fruit even in small containers, but the fruit may be extra small in them. Fruits are ripe when they fall off the plant. I've gotten fruit on Aunt Molly's ground cherry indoors. I don't recommend the Cape Gooseberry ground cherry indoors, however (although it's great for outdoors). You might try Aunt Molly's, Goldie, or Ammon Martin's. Goldie is probably the sweetest (but not the largest). Ground cherries don't seem to need a pollinator plant like tomatillos often seem to.
Basil is a good herb that you can practically use as a vegetable. People grow it indoors a lot. I'm wanting to try Spicy Globe basil (since it grows in a round globe-type bush), but I'm not sure how it does indoors compared to the usual kinds.
You might try a parthenocarpic, gyneocious greenhouse cucumber. I don't know if Monika is a greenhouse cucumber, but mine that I planted outdoors had mostly female flowers at first, and it is parthenocarpic. It's also pretty early. Parthenocarpic means it doesn't need to be pollinated to set fruit (but it does need to be pollinated to produce seeds). Fruit aside, cucumber flowers taste amazing (although they're very small), and they're very easy to grow indoors; if you pick them off, more flowers will probably grow fairly quickly.
Carrots are supposed to be among the easiest vegetables to grow indoors. I haven't tried this yet, but I'd like to some time.
Radishes seem like they would work. Here's a link that tells how to grow radishes indoors. I haven't tried this, either.
Growing green onions indoors is supposed to be workable. You can regrow onion bulbs from the roots, indoors, I hear, but that takes a lot of time (and my attempt wasn't successful, but I didn't give it a south window); so, I mostly recommend it for the green onions, which are quite underrated anyway. You could just use old store onions for green onions, but if I were to try it, I would want to try such as Crimson Forest bunching onions, to see how they do; again, I haven't tried this yet, but it may work. Actually, you might want to try potato onions (like the yellow potato onion, maybe), as they multiply (I'm not sure if bunching onions multiply). Shallots might work, too (and they also multiply).
For most plants, adding grow lights should help considerably. Compact fluorescents and other fluorescents work pretty well. If you only have a few plants, you might try LED bulbs sold as grow lights (with the right wavelengths of red and blue light).
Be aware that low light conditions often invite such as fungal diseases, fungus gnats and such. Using a 2700k CFL wards off damping off disease in my experience, and while 6500k CFLs are probably best for leaf growth due to the high amounts of blue light in them, 2700k CFLs also help plants (they have more red light, which should contribute to flowers/fruiting); they do help leaf growth, too. If you have a fan going (even if it's on low), that should help to prevent a lot of problems, too.
Be sure not to get too many plants indoors without taking proper precautions, because it can make your grow room humid (from watering so many plants) and can potentially invite such as black mold on the walls. A dehumidifier may help (but I haven't tried one).