Martian

So New Balance, but not? That narrows things down quite a bit; you're basically looking for a standard trainer, I gather. Some options straight off the page you linked:

Puma Speed Cat
adidas originals Stan Smith
Reebok Lifestyle Classic Ballistic EXT

Those are all good trainers that might suit you. You can also look at Nikes if you want, but I don't like them myself. I've found they don't seem to wear as well as their competitors. Converse probably isn't a good idea in wet weather, since their All-Stars are almost all made from canvas and I don't know how well that would work in keeping your feet warm and dry. If you're less athletic, you could also look at a pair of skate shoes. I don't really like the chunky style personally, but they're pretty much the word on comfort. A couple of examples are:

Vans Old Skool
DC Belmar

My last suggestion, given based on what little I know about Seattle weather patterns (which are, I gather, quite similar to Vancouver weather patterns), is a hiking shoe. These aren't as good for running or playing sports, but they'll keep your feet warm and dry:

Keen Voyageur
New Balance MR873
Columbia Beartooth

Whatever you get, make sure you don't skimp. I'm not a label snob by any stretch of the imagination (I only have a handful of items in my wardrobe that are from big brand names), but footwear is where I make the exception. Good shoes are worth the extra cash, whereas if you go for the bargain brand you usually end up paying for it. Not only do they tend to wear out sooner, but they're usually not nearly as comfortable either. It's worth it to spend a bit extra upfront and save yourself the headache. Or footache.

__________________
I wake up in the morning more tired than before I slept
I get through cryin' and I'm sadder than before I wept
I get through thinkin' now, and the thoughts have left my head
I get through speakin' and I can't remember, not a word that I said

- Ben Harper, Show Me A Little Shame