Aldi, a German chain, is short for "ALbrecht DIscount". They offer only the store brand plus occasional specialty items from national brands. They have been criticized for quality, but if you are dissatisfied they have a "Quality Double Guarnatee" meaning that they replace the product AND give you your money back. I've never had to do this yet.
Their website also has a vegan and a vegetarian meal planner complete with recipes and nutrition facts! There are about a dozen locations in Columbus as well as Newark and Heath and sundry otherplaces. Enter your zipcode in the top right corner of the meal planner page to find the one closest to you.
Aside from being able to make soy lattés and such upon request, Paneras typically also keep a binder under the counter with ingredient lists for every single thing they serve. Their bagels are vegan except for the ones containing cheese or chocolate or special flavors, and they will bring you a little container of olive oil as a substitute for butter if you ask.
If you want a fancy bagel, the Dutch apple bagel is vegan, as are the obvious sesame, garlic, and "everything" bagels.
Optional multi-vitamin "blasts". Very large menu, so check it out beforehand so you know what all the quirky names include. Be careful though, some have yogurt.
Many smoothies and fresh juices: fruit, wheatgrass, and vegetable.
Beans have no oils or lard added. Burritos, tortas, and tacos can all be made vegan without cheese or sour cream. Unfortunately, "vegetarian nachos" are made with cheese, but the chips and salsa are vegan. Very filling and inexpensive.
Falafel, hummus, babaganoush and garden pitas. Avocado and sprouts are some of many vegetarian toppings. Bicycle or scooter delivery sometimes available to Ohio State campus area.
Any dish can be made vegan by request. Also they offer steamed brown rice as an alternative to the standard side of white rice.