I prefer meeting in the lobby and heading up together....

Whose to say (from an outsider looking in) that you 2 aren't dating? I always prefer for my dates to wait for me in the lobby (rarely happens) but I just feel that doormen or people in hotels always know. Maybe I'm paranoid BPs will do that to you but to me they always know. I would meet in the lobby. Better yet outside hotel and walk in together  

Hope that helps  

Good Luck

and walk her up to the room, but I've always thought that was less discreet than just giving out the room number and having her come up.  I always leave the door ajar so she doesn't have to knock.

I would wait in the room.  Meeting in the lobby is "gentlemanly", but may bring unwanted discomfort to your partner.  Trust me, if she's been providing more than a month, she's comfortable riding an elevator to an upper hotel floor.  Leave the door ajar so she doesn't have to knock.  

I have met several women in the lobby and I always feel conspicuous -- I'm guessing I also look pretty conspicuous.  I'm 58 and white, and once met a 22 year-old AA woman in a very large lobby (convention hotel in a major city -- a VERY large lobby).  She was perfectly at ease, and we were between the sheets 3 minutes after reaching my room, but I had the feeling that hundreds of eyes were on me as we walked to the elevators.  Interesting juxtaposition -- I met the same woman a year later and she showed up at my room without even letting me know she was on premises