I've been called a lot of things in China. Some are sweet. Some are... less sweet. Here's the translation guide.
Lao wai (老外)
Literally: "old outsider." The most common term. Usually neutral, sometimes affectionate. Old Chinese people say it with a smile. Young kids shout it with excitement.
Wai guo ren (外国人)
"Foreign person." Formal, polite. What people say when they're being careful.
Lao mei (老美)
"Old American." Specifically for Americans. Shortened slang. Not rude, just casual.
Da bi zi (大鼻子)
"Big nose." Okay this one IS rude. But small kids say it without malice — they literally just noticed your nose is bigger than theirs. Adults saying it? Less cute.
Yang guizi (洋鬼子)
"Foreign devil." Historical term, mostly joking now. Older people might use it ironically. If a young person says it, they're probably trying to be edgy.
Gao ge (高个)
"Tall person." Descriptive, not really a nickname. But you'll hear it.
Xiao jie / Xian sheng (小姐 / 先生)
"Miss / Mr." The polite terms. Use these for others, expect them back.
What I do:
I've embraced "lao wai." It's what taxi drivers, restaurant owners, and neighborhood aunties call me. It's not an insult — it's just what I am here. An outsider, yes, but one who's welcome.