Mirror's Edge is a good starting place for gameplay, since it matches Assassin's Creed's parkour and melee combat, and Abstergo's white-box aesthetic. However, ME doesn't lend itself to the sandbox very well, since there's only so many ways to create convenient paths between buildings before I lose my suspension of disbelief. At some point, your assassin will either have to jump the width of a 4-lane road or splatter messily on the pavement.
So how do we let our assassin get around a modern boxy city without all those conveniently climbable ledges and ziplines around? The same way every AC game handles anything - new gadgets! A Batman-style grappling hook is the obvious choice, but that would be a bit too easy. A better option might be some sort of glider or wingsuit - it would let Desmond cross large roads or other gaps without falling, but he'd still have to climb normally to gain height, it could believably be concealed in his outfit, and it fits nicely with the eagle motif that all the assassins have.
I can think of a few other non-grappling-hook gadgets. For example, a pair of gecko gloves so he can climb anywhere, or augmented legs (Deus Ex had some really cool roof-hopping sections in Hong Kong) or maybe just something simple like rollerblades for getting around at ground level. As for the classic hay-bales, they exist mainly to get you down from a viewpoint quickly, so how about fast-roping?
The other side of Assassin's Creed is "social stealth", and that's also a lot trickier during the War on Terror, full of metal detectors and keycards and security cameras. On the plus side, it's easier to find a crowd to get lost in. On the minus side, anything important will be locked down tightly, and new gadgets won't cut it here. Perhaps you'll need more of a social engineering approach, recruiting people on the inside who can let you in.
The last part of the problem is guns, but I'm not too concerned about that. The Assassins usually get to close range by sneaking in or blending with the crowd, so nobody knows they're there until they say hello with an extendo-blade between the ribs, then just run like hell. The earlier AC games had bows and guns but that didn't break the game, since you could take them out with throwing knives, stealth, or your own gun, and Ezio could take quite a few bullets without slowing down, thanks to his armor. So give Desmond a belt of knives and a Kevlar hoodie and I doubt anyone will complain.
As for why they would use the hidden blade instead of a sniper rifle a mile away? Perhaps, since the whole "villain's dying speech" is a staple of the series, they need to get information out of the target before they die? I'm sure we can handwave something.
