If you go to Shaolin to train with a monk it is likely a good bet they are as good as or better than anyone in the US (that was not trained at Shaolin or by the Chinese Government) at Contemporary Wushu.
If you are going to Shaolin to learn Wing Chun, Xingyiquan, Tongbei, Changquan or any other CMA for fighting you are better off staying in the US or going to some other part of China and finding a real teacher of these arts. But it is very much buyer beware there are charlatans everywhere looking for the Western buck so be careful. Real good, better than the average, martial arts teachers generally do not advertise and they generally do not speak much English either when you are talking China.
But as to finding the real fighting styles in the US; Well of course you can find them but it is not easy and there are martial artists and martial arts teachers in the US that are as good as any you will find in the East (depending on style in my opinion). But if you can train in the East as apposed to the West in general you will have more time training with your Sifu in China, I cannot speak for Japan or Korea.
My Taiji teacher is from China but teaches here and I am thoroughly convinced I will not find a better one in China or anywhere else, maybe as good but not better.
When I trained Wing Chun my teacher was an American and I was very impressed with his skill and I would not go looking for a better teacher in China either, I might find one that is more skilled in China but I might find one in America too. His teacher is of the IP family and I imagine is better than him and I believe his teacher lives in China. But there is allegedly a gentleman an hour north of me that does not advertise, takes only advanced students is suppose to be very good and was a student of Ip Man and he is in the US.
My first CMA Sifu is also from China and teaches mainly Wushu and he is ok but I know there are better in this country (his wife is a better teacher actually) and much better in China. My first CMA Sifu now claims to teach Chinese martial arts and I know there are much better than him in the same town. My most recent Xingyi Sifu was an American a good fighter and I am certain there are better Xingyiquan teachers than him in both the US and China, but he was not bad at Xingyiquan.
There is good and bad in both America and Asia and you need to be careful when choosing a teacher in both America and Asia. Just because the teacher is Chinese, Japanese or Korean does not mean they are any good.
I went to check out a Hapkido a few years back that was run by a Hapkido master from Korea who I assume was fairly good in Korea but after years in the US his school and his students were pathetic. I have checked out a bunch of TKD schools in my area and I have seen a few run by Korean nationals and the best one in my area is run by an American, who also teaches hapkido I found out afterwards. Iwas invited to watch a class and that too was very impressive.
In Beijing there is now an MMA school run by a retired (I think) LEO from America and he also has a partner that teaches Muay Thai. Is this school not as good at MMA as an American School or is the Muay Thai not as good as you would get in Thailand? To be honest I do not know I do not train either but if you have a school like that in Beijing and advertising it I am guessing you are pretty good because you may get challenged from time to time.
Bottom-line it does not matter where the teacher is from just what he/she knows and in their ability to teach, that is all.