I’ve known for a while that for the highest perceived fluency, a foreigner should aim for a Beijing accent. That’s what Dashan did, and I’ve witnessed many times that a Beijing accent just impresses Chinese people more (especially outside of Beijing). It never had any appeal for me, though.

What I have noticed, though, is that as one’s accent improves, it can move through various levels of perceived fluency, seemingly imitating some of Greater China’s regional accents. I’ve actually heard Chinese people make some of these comments, and I cobbled together this rough guide to what the various comments mean.
When they say you sound like a… they mean that…
老外
(foreigner) your Chinese is bad.

外国人
(foreigner) your Chinese is bad (but they tried just a little to be polite).

新疆人
(Xinjiang person) your Chinese is functional, but your tones are a mess.

山东人
(Shandong person) your Chinese is a bit better than a 新疆人’s.

四川人
(Sichuan person) your Chinese is a bit better than a 山东人’s.

香港人
(Hong Kong person) your Chinese is pretty good, but sounds a little funny.

南方人
(Southerner) your Chinese is good, but some consonants are non-standard.

台湾人
(Taiwanese) your Chinese not only sounds like a 南方人’s, but also a girl’s. (This is not so bad if you happen to be a girl.)

东北人
(Northeasterner) your Chinese is good, but not quite up to 北京人 levels.

北京人
(Beijinger) your Chinese is really amazing.

台湾人
(Taiwanese) your Chinese not only sounds like a 南方人’s, but also a girl’s. (This is not so bad if you happen to be a girl.)

Actually you'd probably have better luck speaking mandarin than english. I just got back from a week long trip in Hong Kong I was under the impression beforehand that everyone spoke perfect english. Booooy was I wrong. Unless you are at a really high class place, you're plum out of luck. Thank goodness I know some mandarin to get around as most HKer's can at least communicate somewhat in mandarin.