Completely depends on what you're looking for.
Do you want a large lot ? Are you willing and able to maintain a large yard?
Do you want a Horse Property?
Walking distance to downtown area
Walking distance to train station (for commuters)
Schools --Fullerton offers a variety of schools --each with its own programs and character. Furthermore, Fullerton schools enjoy open boundaries, meaning you can enroll your child in any school as long as you make the deadline and there's room. However: what's right for one family, might not be right for yours.
If you don't have any children, and don't plan on it, then schools might not be as significant, though a home in a more desirable elementary school area will always be more in demand. Hence, I always say --single people or couples with no children have just as much at stake in keeping Fullerton schools good, as families.
Proximity to either CSUF or Fullerton College
Proximity to freeways (57, or the 91 and the I-5)
Closeness to walking, bike riding trails
Type of house: historic, custom, or track. If you want a historic home: do you have the finances or DIY skills to afford the upkeep? Keep in mind that there are historic neighborhoods that keep very strict control over what you can and cannot do to modify your home. Not all historic homes are in designated historic neighborhoods though. However, also remember that none of the historic homes in Fullerton are affected by the Mills Act.
Fullerton is actually pretty spread out, and it all depends on what you want.