To be in the Carpenter school district you can by anywhere in between Laural canyon blvd and Colfax ave, north or south of the blvd. Some new families would prefer North of the blvd if they have kids because of the flat land they have north of the blvd and less danger from the hills.
I would recommend to purchase a home just north of the blvd close to Colfax ave, there are great homes there in good prices.
Let me give a source that is 100% free to all to look at the market just like a real estate agent does.
Click the link to site in the bottom and take a look at the market in that area..
So "prime" is whatever you prefer. Studio City is Very Unique in that it offers many different kinds of Prime areas. It also enjoys close proximity to major freeways going north/south and east/west as well as Canyons that access the Hollywood Hills, Beverly Hills, Bel Air and the West Side of Los Angeles.
Keller Williams Realty
The above link should lead you to a map of the Carpenter Avenue Elementary School District (bordered on the west mainly by Whitsett Ave, the south by Mulholland Drive...and snakes its way around, as you can see). Some listings will mention the "Silver Triangle," which is another way of saying "bordered by Ventura Blvd, Laurel Canyon, and Laurel Terrace;" the Silver Triangle is contained within the Carpenter School District.
This link will lead you to the school's web page, if you are interested.
As for hot areas, South of the Boulevard is favored because most of the homes are in the hills, but there are some beautiful homes (and a few great deals) on flat land.
Best of luck,