What to do in the vicinity of Los Alamos

Albuquerque

Note that Albuquerque is at about 6,000 ft elevation, and the nearby Sandia Crest is about 10,500 ft (+- a hundred feet or so, depending if you go to the Crest or to the Tram). This is 1,800-3,200 m for the Europeans among you. Unless you are one of those lucky ones who lives in the Alps most of the year, hiking up the Sandia Crest in your first day in New Mexico is probably not the best idea.

Sandia Mountain is a nice hike (La Luz trail) and/or cable car ride (half a day to a day).
Old Town area will take you a few hours to explore (but don't forget that Santa Fe offers a lot more antiquities and Indian artifacts).
Petroglyphs National Monument offers some nice hikes -- better be here early in the day, or the sun will burn you into ashes.

Santa Fe

Santa Fe is a remarkably cultural city for its size. It's the second biggest art market in the USA and the second oldest surviving city in the USA. The best way to enjoy the city is strolling in the downtown, visiting galleries (there are over three hundred of them in the city), and eating at nice restaurants (again, over three hundred, some rated as exceptional and to eat at before you die by Zagat or New York Times).