Okay, I had some additional thoughts while walking.......
There is a safe restaurants thread in Jeff's area. Ethnic restaurants are often veg-friendly, although not oil-free. Some Asian restaurants have steamed vegetables and brown rice. Our favorite is Indian.
Check Happy Cow http://www.happycow.net
for wherever you happen to be. We learned the hard way to verify listings, as they don't necessarily remove closed businesses.
Find the local health food stores/natural foods stores/co-ops. A good many of them have small cafes. Perhaps not oil-free, but vegan is generally available in the hot and cold items. They will also have refrigerated items, which you can tuck into the cooler for later. This also includes the national chain, Whole Foods Markets, which is often discussed by members here. As one who has shopped in their stores in numerous states, let me say this...... they are most definitely NOT all created equal. Some have deli areas that totally offend me, others have so darned many good looking options that I wished I was shopping for them as opposed to groceries!
Explore the local farmers markets once the growing season is underway. Not only will you be able to get delightfully fresh local produce items, but many of them also have vendors who sell prepared items as well. Some local restaurants, for example, have booths at them, hoping to draw diners to their restaurants. Other vendors might be an individual who loves to cook and sells their foods.
With respect to truck stops, I feel fairly confident in saying that if it has a parking lot large enough to accommodate numerous eighteen wheelers, there is a shower and a microwave inside. I have never had occasion to understand the rules with respect to using the showers, so I cannot comment further.
And, LOL, you can always warm something on the engine block!