Other opinions may differ, but I'd gladly pay the $195 to fly into DCA rather than wait on a possibly lower fare, which will likely be into BWI or IAD.
Assuming you won't be renting a car anyway (there's absolutely no need for one in DC), DCA is far and away the most convenient option -- right off the yellow and blue lines of the Metro, which will both take you into the heart of the city. Getting to/from Dulles requires a Washington Flyer bus (it can take an hour if traffic is bad), and BWI -- let's not talk about BWI.
Plus DCA is a far more pleasant airport than either of the other two as regards getting in and out (security is much more professional there than at Dulles, for one, and anyone can guess why!).
Nor would I blow 25K miles on a ticket that you can get for under $200. That's 0.8 cents per mile, not a very good value for money IMO. Save the miles and take your wife to Italy this summer instead.
Mook
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The future of US domestic air travel:
"Please watch your head as you exit the aircraft."