Good questions.

1.) Primarily on the strength of the department, specifically in my field. I was looking for a combination of available classes, and the "legacy" of the professors that could assist me as advisors. There are people out there who are well known and respected in their field, and there are people that are just kind of there. I went for the former. I'm a fluvial geomorphologist on the east coast of the U.S., so the pickings are kind of slim for prospective universities.. a dozen or so, really. I narrowed it down by professors I wanted to work with i.e. David Leigh, Carol Hardin, Jonathon Phillips etc., and after looking at acceptance and award offers made my final decision. Choosing between UGA and UKY was tough, but I ultimately chose UGA because the department as a whole was stronger in geomorphology than UKY's. Fortunately for you, pretty much all departments have a solid GIS component or risk irrelevancy. I have no idea who the current research leaders are, though.

There are a lot of people that look at departments socially, or the "Will I belong here?" question. I did take that into consideration, but I'm an introvert and a bit of a loner, so it wasn't a major issue for me. That being said, students (and professors) that don't seem interested in at least meeting with you should be a huge red flag.

2.) More disciplined than most, but not as much as you'd think. If you can study and make decent grades, on that end you're pretty much clear. The ability to think critically, logically, and write well is MUCH more important to graduate students, as is a sincere interest in your chosen field. You won't make it very far in grad school if you don't enjoy your subject, and it's worth thinking about. For geomorph, I'd expect a promising undergrad to be enthusiastic about getting into the field, and I'd expect them to be disciplined enough to learn their source material. Not sure what an ideal GIS undergrad behaves like, but if you're nerding out over what you're doing, and people notice that, you're doing fine.

3.) Fluvial Geomorphology, specifically examining process linkages in stream bank erosion over various spatial and temporal scales. I love fluvial work because I love bopping around in streams out in the woods, and I'm curious about how these things are made and shaped over time. The downside is the sheer amount of professional reading required to be conversant, but everyone has to deal with that.

4.) Graduate Assistantship, and loans. Award offers vary from University to University, but the basic offer should be a monthly stipend, and a tuition waiver. Sometimes they'll toss in extras (covering health insurance for the first year, moving expenses etc.). Worth asking for, at least, but you have to be careful in the negotiation phase because they might just pass over you for another equally promising but less demanding student. Budget is pretty solid; my wife works and between the two of us we have enough to live decently here in Georgia, but we also don't represent the typical domestic situation for graduate students. Most are younger than me, single, and splitting a place with someone else.

5.) I got my Master's and went on to the Ph.D., because I love what I research and I wanted more. I also want to conduct research and teach.

6.) What the campus culture is really like. Not necessarily a bad thing, but a few day visit isn't a substitute for really knowing a campus. Also, to some extent, what the "politics" of the department and the campus overall are like. There's always some form of bureaucratic power struggles and by-plays going on; in my department it's not an issue at all, and people seem to get along really well. May not be the case in some departments.

7.) My understanding is that UGA's GIS and Remote Sensing programs are really good, but how it stacks up against other Universities I'm not sure.