Embassy Suites Hotel Downtown -- You're close to both a Red line and a Blue line Metro station (the zoo is on the Red line; the Smithsonian museums are on the Blue line) and within walking distance of Georgetown. Your kids can sleep on the pullout sofa in the separate living room. You've got some kitchen facilities, but the complimentary breakfast in the atrium is unbelievable. There are also an indoor pool and a free game room.
Hilton Washington -- A large heated outdoor pool, three tennis courts, and a goodie bag at check-in -- what more does a kid need?
Holiday Inn on the Hill -- Your children can find out what other kids have to say about the hotel by accessing the hotel's website and clicking on the "Bubbles" link, and on the "scrapbook" link from there. Meanwhile, parents can take advantage of sweet deals that provide helpful family touring tips and perks such as free parking and breakfast, for reasonable rates. The hotel has an outdoor pool, a "kids under 12 eat free" restaurant policy, Nintendo on the TV, and soap bubbles handed out to children at check-in.
Omni Shoreham Hotel -- Adjacent to Rock Creek Park, the Omni is within walking distance of the zoo and Metro and is equipped with a large outdoor pool and kiddie pool. Children receive a goodie bag at check-in, and the concierge has a supply of board games (no charge to borrow, just remember to return).