Speaking more generally, terroir can also refer to the sense of place captured by the wine of that region: its weather, soil, grape subspecies, winemaking practises, etc., in other words, its 'soul'.
To which end, many French people traveling in France (and often elsewhere) will make a habit to drink at least a little local wine as they pass through to savor a bit of this 'soul', whether the wine as wine has much merit or not. (Most local wines in France -- and every part of France makes wine of some kind -- either 'don't travel well' or are just, well, average, mediocre wine, good enough for everyday, but not great enough to export.)
Accordingly, one might speak, in general, of the 'terroir' conveyed by other produce as well, and even of a place's cookery and other arts: honey is a prime example, since the flavor (and sometimes its very edibility) relies heavily on the kinds of pollen and nectar the bees have been feasting upon. Certainly an heirloom tomato grown in a small organic 'boutique' farm in Connecticut will have a much different taste and quality than one factory-farmed in the South and bred to be picked pink for ease in shipping. In America, potato chips, some soft drinks, and many baked goods are of types that likewise, don't travel well, and often display striking differences in taste and style as one travels, and can also be said to exhibit 'a sense of place': it's often rewarding to sample a bit of these if you travel cross-country.
Likewise, one can argue that a painting from a painter associated with a small college in Kansas will have a much different overall feeling than one painted by someone living in the East Village in Manhattan, over and above the technical and professional merits of the two artists: the New Yorker's art might be more fashionable, being painted for an audience knowlegable about painting and up-to-date with the latest trends in the medium, while the work of a painter from the Plains States might well be more personal with subjects and style reflecting local interests, even if its merits are not those readily appreciated by the readers of ArtForum. While in some arts the sense of place has eroded with the speed of modern communication (it used to be readily apparent, as late as the early last century, whether a doctor had been trained in Germany or Scotland, for instance), in many cases this is still not so: a good argument for patronizing local artists, local growers, and local wineries (and there are some in surprising places) in any case!