If you are staying at the same hotel, meeting there would be most practical option. However, I understand your desire for wanting to wait for your gf.

As md says, you can't get back airside after landing. For three hours, I wouldn't bother with one of the airport hotels. There's a couple of coffee places etc outside of the arrivals hall. I would hang out there with some work: you can use the free airport wifi. Since all international passengers come out of the one gate in the PEK terminals (i.e. one exit in T3, one in T2 etc), you can definitely just wait for her to come out once she's landed. However, at T3, time between landing and coming out can be up to 45 minutes or more if it's really busy and your gf doesn't have e-gates (which I presume she doesn't).

tb