Some of this depends on when Robin Hood is active. The folk tale has roots going back to about the 13th century, and modern retellings generally make him contemporaneous with King Richard's crusading, which would put him in the late 12th century. In later eras, there'd be more variety of food to be got, more easily.

The focus of good food in this era - and really, for a few hundred years either side - was roast meat, and Robin Hood is very much associated with venison. Venison needs to be hung for a while after the deer is shot or trapped, though, which might well have been difficult for an outlaw who was fairly constantly on the move. Let's assume, though, that he had some sort of stable spot deep in Sherwood Forest which was safe enough to store food in, and in which a fire for roasting could be lit. Roasting was expensive, in terms of firewood used, so it was mostly a method of cooking used by the cooks of the nobility. However, if you're already going to be hung for poaching, robbery, etc, you might as well steal some firewood from the King's forest. It also takes a long time to do - I've spent 5 or 6 hours spit-roasting venison outside - so again, that safe spot would be essential.

Cheese was regarded in England as being a poor people's food (unlike both Ireland, where it was called "white meat", and France, which had a huge variety of cheeses even in the Middle Ages), so from a historical point of view, feasting with cheese would have signalled a lack of resources, and having to fall back on a secondary or even tertiary foodstuff (venison, beef and mutton being the top rank, pork and poultry the second, by and large). However, because it was a poorer food, it was one that the peasants and yeomen with whom Robin Hood dealt had access to - most households would have had a sheep or cow, and therefore would have made cheese. But it's pretty clear that outlaws are not set up to keep sheep or cattle, so they must have either bought or stolen it. Robin Hood would obviously not have stolen from the poor, and by the time you're stealing from the rich, there are better things to take than cheese. Additionally, cheese would keep for some time, and would travel well, so it would be suitable for a roving band of outlaws. Soft cheese is easier and quicker to make; the harder cheeses keep longer. So if Robin - or Friar Tuck, or whoever was going to the markets - was buying larger quantities of cheese, it would have been soft, probably around what we'd call cream cheese or cottage cheese. It might have been flavoured with seasonal herbs.

The bread is an interesting case. Bread - alongside beer and porridge or gruel - was the main form of nutrition for most of the peasantry, and even up to the levels of the nobility, but ovens were a big project to build, and expensive to run. So while a large household would often have its own oven or even ovens, there was fairly regularly only one shared among a village of peasants and yeomen. In urban situations, few enough people would have cooked much in their own homes, and certainly not baked bread; that was left to bakers. In more rural situations around Nottingham, there would probably have been a village baker. The bread itself would have been of wheat, oats, or barley - maybe even rye, although it was usually thought of as being the poorest. Milled flour was put through a series of sieves, with the finest, whitest flour going to the nobility to make a kind of super-white bread called manchet; white food was felt to symbolise purity, and it was certainly a form of conspicuous consumption. So the villagers would have had a relatively whole-grain brown bread, almost certainly baked in one-pound loaves. There are a whole load of laws and ordinances dealing with the one-pound loaf, and indeed it's actually quite difficult to account for how much weight the baking process takes out so that the end product weighs exactly one pound.

Pies might also have featured, again from markets - they would have contained mostly meat, and the actual pastry shell might not have been intended for eating. A very salty pastry crust acts a little like primitive canning, and keeps the contents good for quite some time. Eating it isn't a great experience, though.

The question of what vegetables were eaten is a broad one; recipe books from the era don't tend to record much in the way of non-meat dishes. But foraged greens were almost certainly a thing, alongside seasonal fruits, root vegetables like turnips, carrots, parnsips and skirrets (a long, thin, parsnip-like root), stalks like celery and alexanders (now mostly considered a weed), onions, and various brassicas (cabbages, brussels sprouts, kale, etc). Almost all of these would have been boiled, possibly in broth.

It is very likely that all of this was eaten seated on logs by campfires, or the like. But I like to think that Robin Hood, aware of the way in which the nobility ate, would have served his guests their dinner on a trestle table, with a tablecloth, and with seats with backs to denote status, rather than the benches on which everyone else sat.