My best tip for finding a hotel in Washington or in NYC is - Don't. Stay outside the city where the prices are much cheaper. When we go to NYC, we usually stay in Secaucus, NJ, just a few minutes away.
When we go to DC, we stay in Alexandria or Arlington, VA. There are many hotels located a short walk from a Metro station so getting in and out of DC is simple.
As for finding bargains, always check at least sources: the hotel's website, the hotel chain's 800 number and the hotel's direct number. Its amazing how much those sources can differ. And once you book a rate, that's not the end of your search. Every few days until your trip, keep checking those sources to see if rates drop or specials are announced.
A few years ago, I took my wife to NYC for our anniversary. That was the one and only time we actually stayed in the city at the Rhiga Royal (we're Marriott Reward members). I booked and rebooked 5 times. The price we finally paid was $57/nite less than the price we originally had, so it pays to be persistent.
Steve