What's on City -- TONS of stuff, just about everything in the city is here: every museum & historic building, music, ice skating at the National Gallery of Art's sculpture garden, activities, etc. Click on the calendar date and then a page will appear with a whole slew of classes, events, tours, galleries, shows, music, etc. on the right hand side.
Washington City Paper Arts & Events section -- search by date, keyword or browse talks, lectures, theatre, music, etc.
To get around once there, see maps of DC (includes maps of parks, landmarks, museums, monuments, the Mall and all Smithsonian museums and the metro map for public transportation).
Image from Public Domain Clipart