Almost Famous is set in the early 1970's, but Cameron Crowe makes no attempt to make the movie look and feel like it was actually made in the 70's. There are no grainy filters thrown on in post-production, for example. But given the earthy color palates utilized in the set and costumes, paired with the iconic soundtrack, there's no place in time we could be instead of the 1970s.
The Almost Famous crew actually filmed many of the scenes in their actual locations, including at the San Diego Sports Arena, the Continental Hyatt House in Los Angeles, and the Plaza Hotel in New York (source). Crowe even went back to the street in San Diego where he grew up to film it (source).