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i would like to know why hawaiian airlines flight 15 out of san diego heads north to LA or San Francisco before turning towards hawaii?

There are 9 routes between Hawaii and the mainland. Each aircraft operating at high altitudes must use these routes. That's the reason why the SAN/Hawaii flights head north before going to Hawaii.

You can get a copy of the chart showing the IFR routes between Hawaii and the mainland at http://aeronav.faa.gov/index.asp?xml=ae ... st_enroute
Click IFR Enroute Aeronautical Charts then select the link under Hawaii/Pacific

There is one route to/from the MZB (Mission Bay) VOR via control 1156 which makes a dogleg to waypoint MALIT. However for westbound flights that usually has a stronger headwind compared to flying towards LA and then turning west to DINTY. The other downside to C1156 is it transits Warning area W281 which, when in use, requires aircraft to be above flight level 180 about 20 miles west of SAN.
On really bad wind days I've seen aircraft head to the bay area and coast out at BEBOP.
So, to boil it down to a simple answer the route depends on what the flight planning computer spits out for the least cost route.
Here is the route for HAL15 a couple of days ago:
PEBLE3 SXC DINTY DUETS R576 DUSAC R576 DRAYK R576 DENNS MAGGI3
SXC is Santa Catalina then DINTY which is the first oceanic waypoint on R576 which is a westbound, one-way route.
Today:
PEBLE3 SXC VTU RZS J88 SNS OSI BEBOP R464 BAART R464 BEKME R464 BOARD R464 BITTA MAGGI3
They are going all the way to OSI (woodside) which is in the hills NW of San Jose then to the aforementioned BEBOP. I doubt they will get all the way to OSI, ATC will give them a shortcut to BEBOP somewhere around Salinas.

Two main reasons as to why.

First would be the SIDs coming out of KSAN, which you would have the PEBLE3 or LNSAY2, which turn north towards Santa Catalina or Seal Beach. That gets them out of the airspace in San Diego on a normal, standardized route.

Secondly, there is a preferred route for arrivals to/from Hawaii, which exits ZLA airspace at the DINTY intersection to join the R576 airway. That takes you straight to Hawaii, where the airway ends at the DENNS intersection, which joins up with the MAGGI3 arrival. So Preferred routing gives everyone a common route to fly, let alone a common route from one destination to another.

In KSAN's instance, it will probably be PEBLE3.SXC DINTY R576 DENNS.MAGGI3.

BL.

I've taken this flight a number of times, I do recall once that the military restricted zone was inactive and the winds must have been right, we took off straight west. We intersected the designated course from LA to HNL, I know this because the pilot announced this course shortly after takeoff.

The flight was close to Christmas, so makes since about the military restrictions opening up. Also encountered same situation on a return flight, crossed the shore over the south bay and joined the pattern from the south, I definitely knew this because I live in the south bay of SD.

Alaska is now flying SAN-HNL as well..and the other day they did what John mentioned...went to bay area and coasted out there.
Years ago, Delta ran L1011's on this route. It was a redeye coming back to SAN and most of the time they came direct, entering the left downwind (south side of the airport) for a landing on 27, just as the first departures were coming down the taxiway. AWE has a few redeyes from Hawaii to PHX. Most of them go over LAX, but occasionally one will fly direct via MZB to pick up J18(?) as the sun comes up.