Does any shloka of Gita say anything about what a person should eat. I am mainly concerned with whether it say anything about Vegetarian or Non Vegetarian diet.
Welcome to Hinduism.SE StammeringMathematician! With that name I think you are one of my professors 😄 Kidding.
Here's the most specific dietary "guidelines" I could find in Śrīmad Bhagavad Gītā,
BG 17.8: Those foods which promote longevity, strength, health, happiness, and satisfaction;
Which are juicy, oleaginous, nourishing, and pleasing to the stomach, are dear to those flourishing in sāttva (bright righteousness).
BG 17.9 Those foods which are bitter, sour, salty, very hot, pungent, dry, and overly-piquant;
Which produce pain, grief, and sickness, are dear to those caught in rajas (passion).
BG 17.10 Those foods which are stale, bland, putrid, and toxic;
Which is ort or unfit for sacrifice, are dear do those drowning in tamas (dark destruction).
So, we can dissect this to get a little more clarity on specific foods.
- tamas foods: Foods unfit for sacrifice include donkeys and camels as well as anything which is expiring. Ort are the scraps left over from preparing the meal: the chopped-off ends of vegetables, certain peels & skins, etc. Toxic foods are anything that harm the body. As for stale and bland foods, I believe this includes many meats because we don't like to eat them without first spicing them up.
- rajas foods: I think these are pretty clear. You can tell if something is too bitter, too sour, too salty, too hot in temperature, too pungent, dry-tasting, or too piquant ("spicy" like chilies). If you end up on the toilet after a meal, something was rajas. Personally, I consider pork to be rajas because, if I eat it after a prolonged absence from eating it, I feel very nauseated.
- sāttva foods: Juicy foods include most fresh fruits and many fresh vegetables. Oleaginous foods are often pressed for their oils. This includes most nuts & seeds as well as some other things like olives.
Of course this is no definitive list, but it's hard to be very precise without delving into interpretation. Other than the above, the only other mention of foods in the Bhagavad Gītā is in reference to ceremonial sacrifice or the below quotes.
BG 6.16: Yoga is not eating too much, nor is it not eating at all;
neither is it sleeping too much, nor not sleeping enough, Arjuna.
BG 3.13: The saintly, who eat what remains of the sacrifice, are released from erring;
but the erring, who cook only for their own sake, consume their own impurity.
BG 9.27: Whatever you do, whatever you eat, whatever you sacrifice, whatever you gift to others;
and whatever austerities you undertake, Son of Kunti, all that you offer to Me.
So, keeping in mind BG 17.8~10, I think you can discover for yourself which things are fit for eating, and which aren't. Just don't forget BG 9.27 & 3.13; when you eat, remind yourself that it is a sacrifice to God within you. And also per BG 6.16, eat in moderation.
As per Bhagavad-gītā, food is of three kinds: Sattvic, Rajasic and Tamasic. This classification is defined in 17.7 to 17.10.
रस्याः स्निग्धाः स्थिरा हृद्या आहाराः सात्त्विकप्रियाः।।17.8।।
आहारा राजसस्येष्टा दुःखशोकामयप्रदाः।।17.9।।
यातयामं गतरसं पूति पर्युषितं च यत्।
उच्छिष्टमपि चामेध्यं भोजनं तामसप्रियम्।।17.10।।
17.8 Foods that augment life, firmless of mind, strength, health, happiness and delight, and which are succulent(juicy), oleaginous, substantial and agreeable, are dear to one endowed with sattva.
17.9 Foods that are bitter, sour, salty, very hot, pungent, dry and burning, and which production pain, sorrow and disease, are dear to one having rajas.
17.10 Food which is not properly cooked, lacking in essence, putrid(emitting a bad smell) and stale, and even ort and that which is unfit for sacrifice, is dear to one possessed of tamas.
As per the properties defined in above verses, Non Vegetarian food falls under Tamasic category. And by this narration, it's clear that the food people eat influences their guna (nature) and vice versa. So, it is advised to eat sāttvic food (as much as possible) as other food causes rajo or tamo guna.
The only occasion where Lord Krishna gives specific and explicit food recommendation is Bhagavad-gita 9.26:
If one offers Me with love and devotion a leaf, a ﬂower, a fruit or water, I will accept it.
Those are, obviously, vegetarian foodstuff because Lord Krishna does not accept non-veg food.
Those who aspire to become devoted souls surrendered and dedicated to Lord Krishna will offer him only that kind of food which is recommended to his devotees (his bhaktas) to offer him. As far as I know Hindu scripture recommends bhaktas of Lord Krishna/Vishnu to offer him only vegetarian food. There is no recommendation to offer him meat, eggs and fish. If we browse scriptures for examples of food which is accepted by Lord Krishna from his devotees (bhaktas) we can find only examples of veg food such as those in the Bhagavad-gita verse I mentioned, or such as those like we read in the Bhagavatam 10.13.11:
Kṛṣṇa is yajña-bhuk — that is, He eats only offerings of yajña — but to exhibit His childhood pastimes, He now sat with His flute tucked between His waist and His tight cloth on His right side and with His horn bugle and cow-driving stick on His left. Holding in His hand a very nice preparation of yogurt and rice, with pieces of suitable fruit between His fingers, He sat like the whorl of a lotus flower, looking forward toward all His friends, personally joking with them and creating jubilant laughter among them as He ate. At that time, the denizens of heaven were watching, struck with wonder at how the Personality of Godhead, who eats only in yajña, was now eating with His friends in the forest.
To my knowledge there is no mention anywhere in Hindu scripture that Lord Krishna is offered roast chicken, pork, bacon, fish and eggs, or similar like non-veg food.