Mikael, the AMTRAK will drop you off, in San Diego, at stations by Old Town San Diego and near to Harbor Blvd. Just be sure you know the schedules, as I think the last train out leaves Old Town around 6:30 PM, heading to LA.
I remembered this, as, last May, I drove down to San Diego on Friday afternoon; stayed in Mission Bay and met a friend for dinner.
Saturday some other friends took the train down for Cinco De Mayo (an extremely popular event in Olde Town) and I met them at the Old Town Station; they made sure to be back on the train for the trip back.
Los Angeles to Las Vegas is, sadly, either a driving or flying trip; no direct train service, that I know, goes there.
You can probably fly to Las Vegas from the Long Beach Airport, but I cannot guarantee the schedules. Besides, with post-9/11 security rules and waiting to get on the plane, plus collecting luggage and getting ground transport at Las Vegas McCarran Airport, many of us here in LA realize it takes just as long as it would to drive to Las Vegas; such is life.
My advice: save a trip to Las Vegas or a trip to Mexico for a later venture.
Check on places to see in Long Beach, especially in the Shoreline Village, The Pike shopping area (where a former amusement center used to be located) or near to Ocean Avenue.