It's best to arrange to meet at the hotel room or in the hotel's conference room, if available, and ideally have meetings lined up in a way to minimize back and forth to the expo floor. It's usually too hectic in the expo to get things done.
If your customer has a booth, you can try meeting at their booth's conference room. Convenient for them and cheap for you.
If you want to impress them -and not worry about potential negative perception of being too lavish- you should get a suite at your hotel. They are not as expensive if you book them in advance and they are the best because they have a separate meeting/living room and you can control the meeting and host them in a super private/intimate environment.