- West Edmonton Mall (Edmonton, AB). In one sense, it is the mother of all greybox malls, surrounded by an asphalt moat. But: it's accessible via local transit, and it's very much in the model of an artificial downtown: it contains hotels, apartments, a hockey rink, an aquarium, and a variety of other things not in the simple greybox mall. This is because it gets really freaking cold in Edmonton in the winter and it's nice to go "outside" without going "outside"; and the diversity of stuff that's there keeps it more alive than at, say, Woodfield (outside Chicago, IL). The food court felt less like a food court and more like a street that had a bunch of little food shops on it. Basically, they've adapted "downtown" to the needs of their climate.
- The Ala Moana Mall (Honolulu, HI). I mention this mostly to contrast the previous one. It's laid out like a greybox mall, but since it's Honolulu, they just skip the whole "roof" thing on the central ways. So it's really more like a pedestrian street with a lot of shops on it. Also, it contains (or is adjacent to?) some non-shop things, and it's well-connected by transit. EDIT to add: There are outdoor malls other places, too, and they're sort of in vogue right now. What makes this one different is how well-adapted it is to its surroundings.
- Providence Place Mall (Providence, RI). Built much more recently (1999 or so), it does include a parking deck but isn't surrounded by asphalt in all directions. It's got entrances that are right off a relatively walkable street, with a couple transit connections (and it's about two blocks from the main central transit station). Internally, it feels nothing like a classic greybox mall: it's five stories with shops on both sides, and lots of windows give it plenty of natural light. It felt much more like a part of downtown than an alternative to it.
So basically, it's possible to set up your mall in such a way that it steers clear of the major problems plaguing malls; and there's certainly reason to think that reinvention rather than abandonment is the mall's likeliest future.