1. Case, 2. Baylor (if you're willing to bust your butt for all 4 years), 3. KU, 4. UMn, 5. BI-MS
My rationale:
Case is an excellent, growing, up-and-coming program. They treat their residents well. You start off with an excellent internal medicine education. Neurology education is supplemented well w/ didactic time and a neuroscience refresher course that is really unique to Case. They have huge names at their institution. Their stroke team is godly. Subspecialties are well represented and they send their residents to excellent fellowships. Research is plentiful and readily available. Cleveland, however, sucks. If you can get around that, I'd argue Case is on equal footing w/ Cleveland Clinic, if not better. It's a top program, and with better marketing, would be easily recognized as such.
Baylor has developed a reputation for being "malignant." They are only malignant in the sense that they have a seemingly overwhelming workload. Yet, dedicated residents make it through the program every year. They have great research backing, good subspecialty representation, diverse patient population, and place their residents into fellowships well. The "Baylor" name is well respected in the field. Yet, not everyone wants to work that much, so this program probably isn't for everyone. You probably won't get a lot of time for electives, though, which is a big downside. Still, I would recommend it if you are considering a stroke, NCC, or neurohospitalist career.
University of Kansas is a strong, up-and-coming program, in an up-and-coming city. They keep expanding every year, and University of Kansas is a respectable name, especially in the Midwest. It's a decent sized program with dedicated and intelligent residents, good subspecialty representation, and ample research opportunities. KC BBQ is amazing, and regardless of what anyone else says, is the best BBQ in the country.
University of Minnesota has a lot of resources, but they seemed to have some faculty shifts in the past couple of years. I thought the program had a great feel to it, and provided for an excellent well-rounded education in neurology. Minnesota is cold. Really cold. There is lots of snow. This may or may not affect your decision. They have great facilities though. And the city is pretty happening, and hopefully, they have the Lightrail up and running.
Don't know much about Beth Israel - Mount Sinai in NYC, so I put it last.
Hope this helps, but this is pretty much purely one person's opinion.