Much as I love Haverford (I was a Bryn Mawr grad from before Haverford was co-ed), I would not choose it primarily because it affords the chance to take classes at other schools, including Penn. Haverford is a small, distinctive community based on Quaker traditions of community and tolerance. While Haverford and Bryn Mawr students can take classes at Penn, that only applies to Arts and Sciences type classes – Wharton and Engineering classes are excluded – and is limited to classes which are not generally offered at Haverford and Bryn Mawr. I would discourage selecting Haverford with the idea that it is a “back door” to Penn.
For a student who wants a business major and is not excited by the Haverford culture, Richmond sounds like the better option.
@Midwestmomofboys no i love the haverford culture
Sounds like you really want to go to Haverford. It’s a great college and if your parents can afford it, go for it 
@Anna20021988 Law school acceptance is almost entirely gpa and LSAT scores and most students have to borrow $75,000 a year for 3 years to get through law school, so the general advice – similar to med school – is save money on undergrad to reduce loans and preserve any savings to pay for law school. On that basis, Richmond would be better option.
In terms of access to an exchange program with LSE – exchange programs with Oxford, Cambridge and, presumably, LSE, are usually very competitive for students applying to visit from US schools – the students we know who were admitted to the Oxford study abroad program were the “cream of the crop” at their respective universities. I tend to think that being a big deal scholarship recipient at Richmond would create more opportunities for research, leadership and other skills which would maximize acceptance into a competitive admissions study abroad such as LSE.
You said a tolerant community is important to you – and Haverford certainly meets that. But the other reasons you said you liked Haverford – its location and the opportunity to take classes at Penn (which does NOT include Wharton) does not seem like a strong reason to prefer Haverford.
As I said, I’m a BiCo community member, I think Haverford is an amazing school.
Richmond does have its own law school.
I am a Haverford student and I have a number of friends from Haverford who have taken Wharton classes. I think you may be limited in the number of Wharton classes you can take but I know for an absolute fact that you can take Wharton classes–off the top of my head I can think of five Haverford students in the past couple years who have done it (and these are only the people I know, I am sure there are many more). I wouldn’t really choose Haverford based solely on the ability to take classes at Penn and Wharton but if you like Haverford anyway then I think it’s a plus.
Op, you know that rationally Richmond is better for your purpose but you still prefer Haverford for many reasons, rational or irrational. Sometimes, when you can afford something you really want, you can go for it and not feel guilty.
(The case is different if your parents can’t afford Haverford).
Math at Bryn Maur is better than Haverford and arguably very strong, so don’t overlook what Bryn Maur offers Haverford students, and they can simply walk there, about 1.8 miles, or bus over quickly or ride a bike. . The swimming pool is over at Bryn Mawr. I would look much more carefully at Bryn Maur classes rather than Penn, as its more accessible. The train is not very far to Penn, but more effort. For a business major, math matters a lot. The more math you take the more MBA programs or law programs will accept you, but does depend a little on your law or business goals.
Take as many math classes at Bryn Mawr as you can.
https://www.brynmawr.edu/math/
I stand corrected about Wharton classes – the materials I had read a while ago said BiCo students could only take classes which are not available at H’ford/BMC, but in any event, Wharton School and Engineering classes are excluded. At least from what the website says now, Wharton is not excluded. https://www.haverford.edu/academics/academic-partnerships/consortium-programs
Stll, I would not choose Haverford as a way to get to Wharton as U Penn classes are not nearly as easy to manage as BiCo classes.
Also, very minor, but BMC and Hford are 1 mile apart – we walked it all the time in decent weather.
You say you want to go to Columbia for law school. Wanting and working to get something are very different things. You will need a very high GPA and excellent LSAT scores, as well as excellent EC or work if you take time off. What is grading like at Haverford? Where do you fall compared to admitted student stats? You should look up the common data set for Haverford. You want to make sure you’re going to shine at your undergrad.