Firstly, please forgive me for making this post so 'I want I want I want'. I got a little carried away with the picture in my head.
Weather
The same weather in Paragon City and the Isles gets a little dreary after a while. I remember seeing a picture of St Martial while the Isles were bugged to have Paragon's sunshine. It was oddly beautiful and I'd love to see it occasionally. Not to mention rain.
More detailed character models.
The character creator is currently one of the best parts of the game, and what makes CoH so good, in my opinion. However, other games are catching up with us, and I feel that much more detailed models would almost be a must were there to be a CoH2; separate fingers, separate eyes, waists and necks that can bend independently of each other. Build all the new powersets from the ground up with as much customisation as you can cram in, while you're at it.
A more realistic world
I would love for the city to be a little more... lively than Paragon is right now. In an ideal world, I'd want each and every building to have a purpose. I'd want their interiors to be visible through the windows in the outside world, and to be the correct size for the building that contains it. I'd want each building to consistently use the same map. AE was a great example, but I'm hungry for more. Missions would still be instanced, but we could have a 'ghost' of the interior visible through the windows. I also want a greater variety of buildings, whether heroes use them or not. Markets, schools, clubs, libraries, and I want citizens to use them. I'd also want this new world to be more reactive. Certain big missions (such as finishing a task force) could result in a physical change to the area for a short time, perhaps ridding the area of crime for a while. I also want certain spots that could host a supergroup base. A sewer entrance, an office building, a cave entrance. A great deal many supergroups could share the same entrance so we don't run out of spaces, but having that choice of physical location would be nice. That isn't all, either. I would love for Apartment buildings to work in the same fashion; a building that can hold in as many apartments as necessary, but gives the hero a choice of location. One little thing I'd love here is if we had at least a single window in our apartment instance, where we could look out on to an instanced version of that part of the city, complete with citizens and cars and such. This brings me to my next point in world realism: vehicles. I'd love for the vehicles to behave that little bit more realistically, and even more so if we could have our own personal vehicles. This would be controlled by a vehicle creation system not dissimilar from our character creator.
A bigger world
If asking for a more detailed world wasn't enough, I'd want to expand a little. Perhaps now that Paragon City and the Rogue isles are nearing relatively stable control by their respective leaders, it may be a good time to expand out into the world. Small outposts could be taken in other parts of our world such as other cities, or perhaps outposts in wild terrain. This isn't' so high on my list of wants, but I certainly wouldn't say no. Especially if instead of just exploring to these areas, we could begin our character's careers here. I'd love to be able to play an international hero in their own country.
Nothing else comes to mind now, but I'm sure it will as soon as I've posted. Everything else that I can think of I want to remain fairly similar to its current state in-game. Please keep costumes as a cosmetic thing, and don't make us upgrade to higher 'gear' so we can keep up. I like our power system structure very much, and wouldn't really want to see that changed much either.
Edit some more!: Yes, I know that the game I'm decribing would require a small supercomputer to run. But we were sorta asked. 
I'm hoping for a mutant pack.