Some of these are going to be close to what they are for the stories handed down from medieval times. Some of them, however, are going to have to be different in order to allow faeries to co-exist with humans in the human world.
First out the door is the conflict between faeries and Christianity. Many stories tell of faeries killed by the sounding a church bell, or unable to trespass upon holy land. Still, as we moved more into cities, it seems the faeries came with us and also infiltrated our worship. In Italy, for example, there are said to exist faeries that take the form of little monks that fulfill for the houses of God, the same duties that traditional brownies do in more modest residences. Plus, Christianity is no longer a monolithic entity. Fractured many ways, any power that entity had over the supernatural is diminished. (Though some individuals may be able to focus power to thwart the supernatural.)
Next we come to iron. This might present a problem for the faerie in a modern setting because of the amount of metal that exists there. The traditional weakness, though, is specific to iron. Perhaps limiting it to that would be enough to keep a sense of tradition without overly limiting faeries in a modern setting. Steel, after all, is much more common in a modern setting that straight iron. In some cases, steel is a refined form of iron, but many everyday objects are alloys of iron and other metals. This would, I propose, reduce the effect of the iron on the faerie. So while they might prefer to use tools of wood or non-ferrous metal, they won't be killed by a butter knife.
Other traditional restrictions seem as if they would fit nicely in a modern setting. The obligation faeries feel for reciprocating gifts (which is why you don't thank a faerie for something; the thanks is the reciprocation and a cheap one at that) hold no special problems for a faerie in the modern world. Neither, the feudal structure of faerie society, as it lies outside of any man-made structure. A faerie loyal to its court and Queen would have no undue trouble with human authorities and yet would be subject to interesting plot possibilities. Finally, some stories talk about faeries ability to deceive but suggest that they may not directly lie. (They might tell you about a sign, neglecting to mention the sign is red, but they would be unable to tell you the sign is blue.) This presents interesting possibilities to the storyteller, but I wonder if it might be too restrictive for my narrative needs. I'll table that one for now.
Interestingly enough, the Game of Life I linked to earlier, has a way of infecting my thoughts on this as well. Humans, in my estimation, are what is called a breeder. That is, they grow quickly in population, filling all available space. Faeries, on the other hand, are more often forms of still life or oscillators. That is, they are either stable and do not change or remain unchanged while cycling through distinct states. Interestingly, if you seed Life with a breeder that begins to fill all the available space and then introduce an oscillator or still life, the previously static pattern erupts into swirls of chaotic change. To me, this means the relationship between human and faerie is one of symbiosis. Without humans, faeries would remain unchanged and while the change forced upon them by humans may mean that some of them are destroyed, it is also the only way new faeries can be created. Similarly, left unchecked, humans would fill all available space and would remain stagnant. Faeries in our midst keep us in check but also stimulate our creativity.
The question that confronts me now is: What is the premise of my story? Beyond the "faeries live in a modern world with humans," what is the conflict at the core of my story? This will drive the plot and help determine what characters will be drawn from the setting. Of course, the characters will have something to say about the plot and about the conflict, I'm sure. Left to my own devices, though, I tend to come up with characters that are lovingly detailed but who lack direct motivation. So I'm going to concentrate on the plot first in an attempt to summon from it the characters for whom the action of the plot is critical.