This is Canterbury, an ancient town in the South East of England. Here, as you can see, 1 square mile is enough to contain the entire old town (the oval shape of roads in the centre of the map, bounded in the West by the yellow ring road and in the East by Broad Street and Lower Bridge Street). The old town was encircled by huge walls built during the Roman era and maintained throughout the Middle Ages (and still present in places today). It contains, amongst other things, one of the largest and most famous cathedrals in Britain, numerous other churches, the town hall, the old 15th century library, a vast number of pubs, shops and restaurants, and several museums. Outside of the old town are two railway stations, wooded areas, plenty of houses, recreation grounds, and a university. Clearly, in this 1-mile hex the question is not where adventure could be found, but where it couldn't be.
This is an area of quintessential English countryside, in Somerset. There is a small village in the North East corner - a row of houses along a road - and several farms. While it looks relatively empty, each of those fields is divided by a hedgerow, and the land is flat, making visibility difficult. Travelling across this area would be fraught with tension as, effectively, you would never be able to see more than about 100 yards in any direction at any time, and more often much less.
This is a wooded area in the Forest of Dean, in South Wales. This is, I think, what much of Western Europe would once have resembled - mostly forest, with tracks and roads criss-crossing it, and the occasional glade where trees have been cleared for grazing or firewood. Even though the area is small, it is easy to get lost and even easier to stumble across dangerous wild animals, nefarious forest denizens, and god knows what. The glades would be dangerous to cross, as you would be exposed and plainly visible to onlookers. Naturally, the forest could hide openings to tunnels, ruins, abandoned camps, dead travellers, and so on.
This is Coquet Island, off the coast of North East England. It contains the ruins of a medieval monastery and a lighthouse, and is a refuge for seabirds - there are 18,000 puffins living on it. Clearly, the monastery could be haunted, be the entrance to a dungeon, or whatever else, and the nesting seabirds don't have to be puffins - they could be something more valuable or dangerous.
A Loch, in the Highlands of Scotland. This is rough, barren landscape - not a tree to be seen anywhere, or a scrap of cover except for heather and the folds of the land itself. Here, encounters would take place at a distance, as parties would be able to see each other plainly at great distances. At the same time, adventuring parties cross the area would be completely exposed to, perhaps unexpected, aerial attack. The Loch itself is dark and forboding; does it contain a Watcher in the Waters, the spawn of some ancient god, a forgotten plesiosaur?
A stretch of open coastline on the island of Tiree. Note the airstrip in the North West - not very D&D. There are some tiny hamlets in the West, but the main attraction is of course the bay: a perfect landing point for vessels. Traders, vikings, colonists, explorers?
This is the Southern edge of Loch Ness, in Scotland. Fort Augustus guards the canal which links Loch Ness to other waters further south and allows boats to travel all the way from Inverness, the only city worthy of the name North of Aberdeen, with Fort William, the other major settlement in the Highlands. Fort Augustus itself is small, but includes notable attractions, not to mention a series of locks which control river traffic on the canal. To the East is the rough coast of Loch Ness itself, forested and dangerous.
This is the true wilds of the Highlands, in Assynt, one of the most sparsely populated areas of Europe. This is harsh, remote, and unforgiving landscape, infested with midges, roamed by wolves, bears and who knows what else. In the South West is a deep forest of primeval Caledonian woodland; in the North East is a river with streams flowing downhill into boggy marshland in the North. Cross this wilderness at your peril.
If 1-mile hexes ever feel too small, or you find yourself leaving them blank on the map, think of this post and refer back to it in your mind, and give yourself a good sound spanking for ever having been so foolish.