I would definitely plan on getting out of the airport, and my goal would be to go someplace else (if not downtown, then maybe hiking near the great wall) during at least part of the layover.

But, I can certainly relate to the jetlag variable that those early morning arrivals entail. You might feel great, you might feel awful....or somewhere in between.

As such, if I was in your shoes, I'd probably try to book a dayroom near the airport, to use to put my stuff, get cleaned up, and maybe nap a little, if desired. Then, decide where want to go, and head out. Whether or not the train or taking car makes the most sense depends on the destination, but if you wanted to check out something like Gulou, for example, the train + line 2 is pretty straightforward.

ETA: I just noticed that you don't have a visa. A hotel booking (not necessarily prepaid) would definitely help you get an entry permit. The Hilton is probably overkill unless you fancy spending a solid portion of your time at the hotel. On the flip side, be mindful that some of the hotels on the other end of the price spectrum aren't especially convenient, in spite of the fact that that their names include "airport". There is definitely a middle ground, though.

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