What are some Routes to riding from Los Angeles to San fransisco?
Friends who have ridden the coast from Vancouver, Canada to the Mexican border used Adventure Cycling Association maps for the route. ACA has a series of maps that cover the route.

The ACA description of the terrain for LA to SF matches what I heard from my friends: lots of climbing.


  TERRAIN
  
  This route segment is generally hilly, with lots of ups and
  downs following the coastline in the northern part of the state. Some
  sections in the southern part of the route are rolling to flat,
  especially along the various cities' bike paths along the beaches.


From what I heard about the ride, it was tough enough with (multi-geared) road bikes. I suppose, theoretically, it could be done on a fixie. 

If you look around the Web, there are many sources of bicycle route maps. California Bicycle Coalition is one such example. I have the SLO County map which they link to, and it's an excellent map. Don't miss Turri Road when you go through there.

There are also many threads over at BF regarding this trip:

San Francisco To Los Angeles thread;

Advice for Los Angeles to San Francisco thread;

Considering Riding From Los Angeles To San Francisco thread.

Just to provide a few. Lots of experienced answers in those BF threads...