I'll admit to being a bit lost about what to do thanks to the dub requirement as I almost exclusively watches subs. However, I second Cowboy Bebop, it's a very good and accessible show and pretty much considered the benchmark for good dubbing. Also, who doesn't love space western/yakuza drama?

Also, Azumanga Daioh is a very funny slice of life show about a rather eccentric group of high school girls and their just as weird teachers. It supposedly has a good dub, but I wouldn't know and might just be making that up as an excuse to recommend a show that I love.

Finally there is one show that I enjoyed and actually watched dubbed, Big O. It's basically Batman with a giant robot in a city that's a bizarre fusion style and fairly modern technology. It does have the problem of growing rather weird in the second season and not having all that clear an ending.