Close friend of mine goes to St.Lawrence, I go to UR and almost applied to Hamilton (until I realized there'd be no way to afford it...) so I know a fair bit about all three.
St.Lawrence is a notch below Hamilton and UR academically. If Hamilton and UR (and Colgate) are matches, St.Lawrence is probably a safety. With that being said, it still draws alot of students with its amazing location for outdoorsey activities, merit aid, and high quality academics.
When I started my college search, I almost exclusively considered LACs. The more I learned about UR, the more I realized that small research universities really offer the best of both worlds. While classes at UR will most likely be larger than SLU/Hamilton/Colgate, they are small enough where they allow you to develop a personal relationship with your professor (if you seek it out) and there are plenty of opportunities to take discussion based classes as a freshman. I'd imagine that after freshman year it'd be hard to notice much of a difference (if any) in class size.
With that being said, UR also offers top graduate programs across the board and since the undergrad population is smaller than most institutions with grad schools at this level, undergrads have ample opportunity to work with professors on research. I'm an Econ and Applied Math double major, but I also have an interest in Middle Eastern Studies. When I asked my Polisci/IR professor if I'd be able to work as a research assistant next year even though I wasn't majoring in the department, she was completely on board (UR has a top 15 polisci grad program, FYI). I know plenty of other students that have worked as research assistants even as freshman (and most departments offer opportunities for independent research once you have the necessary coursework). Though I don't know personally about research opportunities at LACs like SLU, Hamilton, and Colgate, I'd imagine that we have more research opportunities, or at least more substantive ones (And we have a top ranked hospital walking distance a way)!
I don't think you should choose one over the other because you think one is significantly better/more prestigious than the other. Your really splitting hairs in terms of intelligence of the student bodies and strength of academics. I think UR's biggest problem is lack of name recognition, but again since Hamilton and Colgate are LACs they don't really fend much better in that category. Depending on where you live/what you study any one of them could be more prestigious than the other.
I'd say Hamilton and Colgate win in location, but that's probably biased because I've lived in/near Rochester my entire life and I really wish I could have gone to a school with more opportunities to explore the outdoors. However, I do think that the city of Rochester gets a bad rap as being a crime ridden city that's a horrible place for college students with nothing to do..alot of music performances, quaint coffee shops and stores, University sanctioned bar parties etc. and Rochester isn't more dangerous than most other big cities (but admittedly probably more dangerous than SLU/Hamilton/Colgate)...
Financial aid: Hamilton and Colgate don't offer merit aid. SLU and UR both do.. I know UR has a need based financial aid calculator you can use on their website. Don't have experience with the other schools so I can't say how they compare.
If you have any questions about UR in general, or specific questions about the econ/math/polisci departments feel free to PM me.
Last edited by CollegeXC1993; 06-22-2012 at 10:30 PM.