I disagree about applying to 20+; it seems like a lot of really competitive applicants apply to 20+ as a safety net, but don't end up filling out all of the secondaries, going to all of their interview invites, etc, and thereby waste their time and money.
You can think about location, you can focus on schools that have a strength in your area of research, and you can consider other factors as well based on hearsay/school profiles and other such things. However, (as is commonly said about undergrad), you can't judge an MSTP without visiting. Nor can you predict who will and will not be interested in your application, regardless of your "stats". I feel pretty strongly that applying to 20+ is not only acceptable, but a good approach.
Here's my story which is one of many and varied experiences people have had with the app process. If I had applied to 10 schools instead of 20, I would probably be at University of Cincinnati's MSTP. Not that this is bad, but I would say I've done pretty well ending up, instead, at WashU.
I had connections with MSTP directors at three schools, I graduated from the undergrad of a 4th, I had alumni consideration (med school, not mstp) at a 5th, and my research mentor knew adcom people at 3 more. Of these schools, I received an interview at 2, and was accepted at one (Univ. Cincinnati). This would have comprised my list of ~10.
I received interviews at two top schools where I would have had no opportunity to pursue a PhD in the field I'm interested in (math modeling). I'm attending WashU, literally the last program I added to my list because their MCAT averages from MSAR were significantly higher than my score, and their math modeling faculty is sparse (according to the internet, and word-of-mouth). Oh, and it's in crappy St. Louis.
And guess what.. while there is no formal biomathematical modeling dept here, there are some very well-recognized and visionary faculty members in this field scattered around the university. I love it, and I dont think there's a better place in the country for me. St. Louis? It rocks. Forget all the rest who say otherwise.
I only interviewed at 8 of 20. I received a bunch more interview offers, but you take them or leave them. It's not a "waste" of time and effort if you don't go to all the interviews. Applying / paying is just part of the game to find where you'll be happiest. It doesnt make any sense to avoid spending an extra $200-1000 when you're applying to fully funded MSTP programs. You'll recover your "losses" in the first month of school. Some schools offer interviews primarily in the fall. Others don't start til january or february. Some have 2 dates, some have 8 dates. There are a few great schools that tell you their decision immediately --off the top of my head, WashU, University of Washington (can be the day after!), U. Wisconsin, U. Michigan.
Conclusions:
1. You may think you know where you want to spend the next 8 years, but you really don't until you get there. So apply to a bunch.
2. App fatigue; after secondary #6, the essays start repeating themselves (EXCEPTION: see Duke, Stanford, USC-Keck). Also, MSTP interviews are a blast, they're very social and the programs generally treat applicants very well. (very different from MD interviews)
3. This is a huge crapshoot. If you want to find the best place for you, apply to lots of schools.
to you. 
