In the period you're inquiring after (say 1st, 2nd century A.D.), Roman soldiers would be provided with grain (about 26 kg per month). Additionally they'd receive pulses (e.g. beans, peas), vegetables, fruits, nuts, cheese, meat or fish, sour wine or vinegar, olive oil, and salt. Acquisition, transport and distribution of these materials would be arranged by the regional or provincial administration.

Much of it would be obtained locally as taxes in kind, tribute, or enforced purchase (at a price determined by the Romans), but some of it would come quite a long way: in Britain evidence of olives and olive oil from Spain and wine from the Mediterranean (as far as Greece) has been found. And to Vindonissa in modern-day Switzerland "were sent oysters from Portugal and the English Cannal coast, wines from southern Italy and Sicily, and oil from Spain." (Kehne, p. 325)

Soldiers could add to the provided supplies by hunting and fishing, as well as trading with camp-followers and locals. Obviously there would be a lot more variation here. They could get whatever there was on offer locally, so this will have changed depending on where the soldiers were stationed.

The above applies to most soldiers, who stayed in military camps. In the more populous areas, especially in the East, soldiers might not stay in camps but they could be lodged with or housed by locals; the locals housing the soldiers would then be responsible for providing all of the required food (with monetary compensation by the Roman treasury). This means their diet would be whatever the local diet was (likely still mostly grain though).

Sources:

P. Erdkamp, War and State Formation in the Roman Republic, in: P. Erdkamp (ed.), A Companion to the Roman Army, Oxford 2007, p.96-113 P. Herz, Finances and Costs of the Roman Army in: P. Erdkamp (ed.), p. 306-322 P. Kehne, War- and Peacetime Logistics: Supplying Imperial Armies in East and West, in: P. Erdkamp (ed.), p. 323-338

The principle source of calories for a Roman soldier was grain, which was provided for by the Empire. The daily ration of this was two sextarii which has been estimated to be somewhere in the neighborhood of 1kg to 1.4kgs, depending on which scholar you ask. On the march this would have been ground into flour by the legionary, perhaps sharing the work with others in his contubernium or squad. We know that on the march each contubernium carried its own mill on the squad's assigned mule, but in the established garrisons there was often larger central mills though if these were worked by a designated miller or by the legionaries themselves we cannot definitively say.

Besides grain, meat, cheese, vegetables especially lentils & beans, oil, vinegar, wine, and salt made up the portion of the ration that was known as cibaria. This was also provided for by the Empire through a combination of import and local purchasing.

In the past it was thought that the Romans didn't eat much meat and you'll occasionally still find references to that effect, but the truth is that meat was a staple of the Roman diet, at least so far as the military was concerned. Exact numbers cannot be pinned down, but Roth SWAGed about .5lb based on Late Roman and modern practices. Beef bones turn up at digs most often with pigs close behind. By the time that the Romans were turning the Med into their own personal backyard pond, both were to be found pretty much everywhere that the Romans cared to take. Caesar relieved the Gauls of huge herds, Jugurtha had to turn over cattle as part of his surrender, as did the Quadi after M. Aurelius was done with them. Pigs were usually turned into salted or boiled pork, bacon, or sausages, with an emphasis on the salted pork since it could be transported well for long periods of time. Since they could be found locally, a legion on the march could plan based on an assessment of the area on foraging local beasts, though if such endeavors were judged to be insufficient to meet needs or if we're talking a peacetime garrison, animals would be driven to the location. Better to make the food walk itself than move it on a wagon as it spoils. Within the legion, individuals were designated as butchers and gamesmen, so the Romans certainly considered meat a staple.

Vegetables get even less treatment in period sources with regards to military rationing, but the Roman civilian diet included beans, lentils, peas, turnips, garlic, and herbs. Obviously most of this would have to be locally sourced but the things that could travel well like beans could be brought up to mitigate slim local pickings if needed.

Cheese is also seldom mentioned, though digs at certain garrisons have yielded equipment for cheese production.

Olive oil could be locally sourced in some areas, Caesar included it in his Commentaries among the spoils of his foraging expeditions, but we know that this staple was imported to many legionary bases throughout the Empire. So much so, that when Aelius Gallus' Arabian expedition ran out and had to resort to using butter, it was considered a hardship.

Romans soldiers typically drank a type of sour wine mixed with water called posca, along with vinegar and what we more commonly think of when wine is mentioned. We know from sources like Livy that wine was carried along in the baggage of maneuvering armies yet also compelled from locals as needed. As liquids are a royal pain to transport long distances, wine was locally acquired for garrisons whenever possible. Beer was also occasionally consumed along the Northern frontier, but that was dirty German water and should be eschewed by all good true Romans! Seriously though, there is no evidence that beer was a part of issued rations though it was consumed at legionary bases.

Vegetius, Appian, Caesar, and pretty much everyone else that talked about Roman rations in the period included salt in their lists. Just like modern Soldiers with our electrolyte-filled sports drinks, salt was critical to a Roman in the field for replacing losses from sweating profusely which strangely enough is common when tramping around in armor with thousands of your best friends. The importance of salt is attested to by Appian's recounting of the surrender of the Salassi in 35 BCE to Octavian's general Vetus after he cut off their supply.

So far everything I've mentioned would have been provided for by the Empire. Seeing as doing so would keep its soldiers chugging along at their duties, the Empire made certain to provide sufficient food to sustain the men with a diet of a bit over 3000 calories per day. Obviously estimates vary as no doubt did practice during the centuries that the Romans were doing their thing, but that figure is based upon modern U.S. Army standards and classical records of legionary size and stature. The diet in peacetime would have had a baseline of "normal" Roman cuisine with a distinct local flair, and on the march the rations would be repetitive Roman marching food punctuated with sporadic local food gathered through organized forage and plunder. During both the individual might have opportunities to improve their diet; in the garrison by purchasing food from the surrounding civilians and on the march by buying from the merchants that often followed armies on the march or even through individual foraging. Sallust for instance related an incident where an individual auxiliary soldier was allowed to set aside his duties gathering water and gather edible snails. Fruit was an item that might be acquired individually as well. "Marching, marching marching. Hey, an apple! Marching, marching..." In fact, though fruit was not included among rations, the Roman military oath included a proviso that stated that fruit was an item that an individual could take and not be compelled to turn over to the commander.

Except where otherwise cited, much of what I know about Roman logistics comes from Roth's The Logistics of the Roman Army at War. A fascinating tome if like me you're interested in the minutiae of ancient warfare.

Has there been any evidence found of garum at garrisons?