Exactly - meet in the lobby
If your worried just buy some of those cheap A4 files and carry them with you - then it looks like a business meeting 
Once met a girl in a hotel - she said she would be down in a minute to get me so I just sat in reception leafing through them - looked proper legit !!!!
I remember being at a business meeting with a bunch of guys in a Sheffield hotel a few years ago. We were in the lobby with a drink waiting to go into the restaurant together. A guy across the way was flicking through his papers just as you described when his female "business associate" turned up and greeted him, and they got up to go up the central stairs together. Now we never said a word, but all had female colleagues and were familiar with their dress and demeanour, so we just looked at each other and smirked. This lass, quite fit, was in a dark suit, but the skirt was a bit too short, the heels and bit too high, the make-up a bit professional and it was confirmed when, walking up the stairs, we saw the seam up the back of her legwear. The decision of the jury at that point was unanimous
But the serious points: first, the vast majority of those in the vicinity didn't even notice, second, as regards us, all we thought was "fair play mate, I'd rather have an hour of that than my fillet steak" and third, no-one including any staff cared a jot. So happy punting.
