My husband is using a shoe called a Brooks Beast... and he's also just
over 300 pounds. However, they are not traditional brown/black style
office looking shoes.

He walks quite a bit, usually a couple miles a day and has been very
happy with them so far. I think he's had them at least 6 months or so.
You might try googling and see if you can find some at a nearby shop
to try on, since shoes are a very individual thing.

Not sure what kind of wear you put on your shoes, but I really really
like New Balances.  I started wearing them a few years ago before they
really boomed because they offer running shoes in extra widths, and I
prefer those.

They have a lot of running shoes, but they also have walking/lifestyle
shoes.  Not sure if there's anything dressed up enough to use for a
real formal job, but they definitely have shoes that don't look like
kickback lazy shoes.

Also, if you walk enough, you might get a little pain in your shins/
knees.  If that happens, you might want to consider having your
posture and gait analyzed (most large athletic stores have machines
for it) to see exactly what shoe would do the best for you.  At the
least, treat yourself an extra $20 and buy some nice soles for the
shoes.  It makes a world of difference!

I agree with James - go with the New Balance. You can get a better fit
with New Balance than just about any other athletic/walking shoe.

Try to get the shoes at a New Balance store - their employees are
trained to fit you to the right size of shoe

Also, a store like  http://www.footsolutions.com/  would be invaluable
to a big guy. I am 280 and I blow out pairs of Nikes like nothing.