Very cool idea, congrats on the launch! I'm an avid traveler myself so I'll definitely be giving this a try! A few things to consider:
1) Before I can even see what the product does I had to onboard, which is somewhat unusual for a website. I'd consider letting people do a few things before you make them onboard so they can understand what is on offer.
2) It's be helpful if you link to the sources for your stats. Some things like "healthcare rate" aren't really intuitive or commonly used, so linking would be helpful. For that one in particular you may want to call it "Healthcare Quality" instead.
3) It'd be nice to be able to compare more than 2 cities at once.
Keep on going - I could see this growing into a popular tool!