I think your thought process is on the right track as to the career tradeoffs. columbia is obviously a broader curriculum. personally I think it is better to have classes in economics/budgeting/management. NYC would definitely get you beyond the DC bubble and broaden your perspective, and so would the school, since a smaller fraction are American and/or studying security. if you want to blaze ahead in the security world and never look back, then georgetown may be the better choice. have you asked what the state dept employees think?
bottom line, you seem to understand the + and - 'es of the choice, but still have the same tough decision.