The first two cities you mentioned both have strong architecture and great museums. DC has a lot of monuments and Chicago has a lot of great buildings, Millennium Park and the lakefront. A wide angle zoom, a fast prime and a tripod would be a good starting point.
I live in Chicago and would recommend the following as possible things/places to shoot:
1. Millennium Park, especially a sculpture named Cloud Gate which we locals refer to as the Bean
2. If you want a nice shot of the skyline from the lakefront, right by the Adler Planetarium is a great view of the lakefront / city
3. Willis Tower (formerly the Sears Tower) has sky decks that jet out a few feet on the 103rd floor -- great views of the city
4. If it is closer to spring, consider the architectural tour on the Chicago River
5. If you have any interest in shooting photos of Jellyfish, the Shedd Aquarium has a nice (but small) exhibit through May of jellyfish in tanks against very colorful backdrops