You need time to get from one place to another, so you'd have less than a day in most of these places, especially if the seven days includes the day you arrive and the day you leave.

Beijing and Xi'an is probably enough for your trip, though a stop in Luoyang might fit on the way to Xi'an.

FRom Beijing have the direct train to Taishan mountain,yes,one day in Taishan probabaly too rush,unless everyone is perfect fit and took the cable car

How about Hushan instead of Taishan?

Luoyang longmen grottoes is great,i like it a lot,Baima si temple is nothing special

Luoyang you could done on your own,rent a audio guide

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Sorry, this is WAY too rushed. You're way too optimistic.

I would be able to help you with SOME train tickets, but not all. You'll have major problems getting sleepers out of Taishan.

If you're only having 7 days, I would strongly advise you to stick to Beijing and only 1 other destination.

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