Good luck on checking in at 11.30am (unless you're a Elite member of a chain hotel) You'll most probably be allowed to drop your luggage off and get a chance to experience PEK for a while. During summer heat, probably better experiencing a shopping mall on that time of the day

Assuming your hotel is NOT terribly off the grid and only reachable by taxi or (local) bus, I'd say suggest to her to take the airport express + metro. It's not rush hour when she arrives, and indeed it's not difficult at all for someone who is at least half-street smart to find any place within the (reasonable) inner amount of Beijing. You could still offer to pick her up from the Airport Express (that would probably be a reasonable compromise) or from the metro station next to the hotel of your choice.

Alternatively, I think the main options for staying at PEK for roughly 3hrs have been mentioned already.