I think SoCal Bong has the right idea; go as far away as possible, to a city you would like to go to but are least likely to visit. Let's look at your choices:
Buffalo
New York
Miami
Philadelphia
Washington
Kansas City
Denver
and one TBA, either Baltimore, Pittsburgh, Cincinnati or Cleveland
Personally I don't have a burning desire to visit Buffalo, KC or any of the AFC North cities, so that would eliminate those for me. Whatever reasons there are to visit Philly, Washington and New York would have stronger cases for similar reasons. New York is a fantastic city to visit but it's easy enough to do already if you live in CT. Although it's a little further away, same goes for Washington.
That leaves Miami or Denver. Denver's about 500 miles further away from you, making it more expensive to get to and therefore less likely that you would ever visit there. Personally, I would take advantage of the opportunity and go to Denver.
Whatever you choose, congratulations and have fun.