2. Be ready to speak cordially about the other programs to which you've been admitted. If you've been admitted to Harvard to work with Prof. Famous Scholar don't be afraid to tell your potential advisor at Yale if the subject comes up. You never know when you'll hear, "Oh, I worked with Famous Scholar on a book some years ago - here are my thoughts . . ." This could lead to an incredibly useful conversation.
3. Be honest about the status of your other applications. Most of us applied to a lot of programs and were admitted to a handful of them. Rejection is a part of the process. I can't repeat this enough - there is no such thing as a safety school for many graduate programs. It is more about "fit" than your 4.0 GPA and perfect GRE scores. Your potential advisor likes your writing sample - really wants you in the program and has some sway over the admissions committee - you're into our program. If nobody cares about your research topic, good luck - even if you graduated from the University of Chicago with a 4.0 and have numerous publications. A gracious way to say this would be, "I applied to seven schools, but have only had a chance to visit four - and so far I've been admitted to . . ."
4. Research the department/program website before visiting. Who are the major scholars working in the department you'll be visiting. Try to get some idea of who the scholars outside of your specific field are - but don't stress over memorizing names.
5. Take a look at some maps of the area. One of us had an experience where we were taken out to eat by a group of graduate students just a couple of blocks away from campus - but became so engrossed in conversation, we had no idea how to get back to our hotel. This isn't a huge deal, but take a quick look at a map before you visit. If the program is in a cool region, schedule a bit of extra time to travel around if you can.
6. Don't just speak with faculty, try to speak with a couple of graduate students. Go out for coffee with a few graduate students and let them dish about the program. Tell them about your interests and ask them what they are working on - pretend to be interested, even if you're not. Ask them about funding in the department and at the school itself. Ask about how well the faculty get along. Where do they live in the area?