We were looking for a relatively small school for our youngest (who started a couple of weeks ago), so I suppose that we just went through this.
We didn’t look at either average cost of attendance or graduation rate. We looked at academic reputations, what programs a school had and the strengths of different programs, the location, and the cost focusing on what is was likely to cost us. We visited multiple schools in both the US and Canada (we live in New England, so Canada is not too far away), and tried to get a feel for what each school was like. We hung out in libraries and food halls and watched the students. We got tours of multiple schools and for the smaller schools the tours were all given by students.
We also looked at what it takes to get in. Schools where you can get in based on grades and SAT scores and references were a plus for us. Schools that look at other more nebulous factors was a negative. One school (a prestigious LAC in the US) that we seriously considered based on scatter plots had accepted one student from DD’s high school with a 3.5 UWGPA and 1100 SAT, but rejected two students with a 4.0 UWGPA and 1250 and 1450 SAT – this apparent randomness was a turnoff, particularly since DD’s scatter dot was going to be quite close to this last student.
The general feel of the school was a major factor. If they stressed “prestige” this was a big turnoff as compared to for example stressing “academics and listening to what students need” – this can be a subtle thing. Location was a major factor. The possibility of avoiding all debt and graduating with funds left in the 529 plan was a factor also. General helpfulness of the people that we dealt with and of the professors with whom DD had interviews was also a factor (at several of the Canadian schools the tours included individual discussions with professors).
In the end we (particularly our daughter) ended up picking several excellent small schools in eastern Canada to apply to, got accepted to all with merit aid, and has started at one of them.