I mean, seriously. You barely get to figure out anything yourself. This is my idea of how it should work.
You start on a map of the world, deciding which clue you wish to go to. Of course, there are some dead ends, with no clues, but they always lead you somewhere. There's no specific order to do it in, no "missions". When you're at the airport, there's usually a list of places to visit. This usually consists of museums, libraries and landmarks. For example, if you looked for a clue in... say, Amsterdam, you could go to the Anne Frank house, or maybe the Maritime Museum. Then, you research the information, and, usually, you'll find hints. Okay, let's take a random Dutch guy: Vincent van Gogh. He'd be an obvious Janus, and you'd go to the Museum (researched it, actual place). There, they will let you look at all the exhibits, and a small notebook (or the PDA) will automatically jot down all information you can find, so you can look at that whenever you find information. YOU get to decide where to go, if you ever find something. Maybe, after looking there, you discover a short code. You can stash the code in your notebook to do later, and then travel to somewhere else; the Museum of Modern Art in New York City, where the Starry Night is being shown. And maybe the thing could allow you to communicate with other players. You actually get to explore the museum, instead of just clicking on stuff. After reading the information, you find it was painted from the view of Saint-Remy-de-Provence in Southern France, so then you travel there. You could have gone there from the start, but then you wouldn't have information. Then, the code, which is a substitution code, if you know what that is, and to find the key word, you must look through your notebook. The keyword becomes "sunflower". This makes the code:
So the code says WSQWQRG. You may mistake the answer as VMJVJKW. That clearly makes no sense, so you could choose to give up on the code. As it turns out, you have to work it out the other way, which makes Gauguin. Any person who remotely knows Van Gogh knows that Paul Gauguin was a roommate, and for Cahills, you know he's a fellow Janus. After discovering a bunch more stuff, you find the next clue: Cypsela, also known as sunflower seeds.
Well, I may have focused more on making a new clue than making a new style of playing, but meh.
Add your ideas in the comments.