If you want a good chance at merit aid, you should first identify colleges that offer merit aid and then focus on those schools at which your child's test scores are above the 75th percentile. This information is reported on every college's Common Data Set. Google the name of the college with "common data set" to find that info. Here is Villanova's for 2012-2013:
http://www1.villanova.edu/content/villanova/enroll/statreports/_jcr_content/pagecontent/download_5/file.res/CDS_2012-2013_v4.pdf
There's lots of interesting info on these forms, but on page 7 the SAT scores of the freshman class are shown. (GPA info is also shown, but because colleges often recalculate GPAs, it is sometimes difficult to judge a student's GPA against those reported by the college.) So sticking with SAT scores, to have a shot at merit aid, you will want your child to have scores (and GPA) above the 75th percentile scores to have a good chance of merit aid.
Whether or not Villanova offers merit aid, and how much, is found on page 18. Line n--Number of students in line a who had no financial need and who were awarded institutional non-need-based scholarship or grant aid (exclude those who were awarded athletic awards and tuition benefits). Here you can see that 91 freshman (out of 1642--from line a) were awarded non-need-based (that is, merit) aid. That's 5.5% of the freshman class. And on the next line you can see the average merit-based award--$13,622.
Fordham doesn't have the 2012-2013 common data set on the website yet, but the one for 2011-2012 is here:
http://www.fordham.edu/images/academics/institutional_research/cds_pdfs/cds_2011-2012_(5apr2013).pdf
The freshman class's SAT scores are on page 13--they look very similar to Villanova's. Merit aid is on page 24. In 2011-2012, 470 of 1943 freshmen got merit aid, or 24%, with the average award being $11,737. However, don't forget to look at what share of all undergrads (including freshmen) get merit aid. At Fordham, it's only about 18% (1448 out of 7804). That means that a lot of freshmen get merit aid but then don't get any their sophomore year--the old bait and switch.