Also consider taking the Coaster to the Poinsettia Station in Carlsbad and Uber on to Legoland. The Coaster runs more times a day than Amtrak. It is a commuter llight rail, so its schedule is heavily weighted to morning and late afternoon. Amtrak and the Coaster use the same rail so from San Diego you can take whichever comes first. From Legoland, you need to decide whether to go north to Oceanside, which is both a Coaster and an Amtrak station or to Poinsettia which is only a Coaster station.

From the Legoland website:
PUBLIC TRANSPORTATION

The Oceanside Amtrak Station (7.5 miles)
Carlsbad Poinsettia Station (3 miles)
Carlsbad Village Station (4.5 miles)
Guests then travel to the Park by cab.

The tracks run close to the shore much of the way with particularly pretty views as the train goes thru Del Mar. They can also stop at Old Town State Park on their return to San Diego or use that as a separate outing another day.

This is an excellent suggestion, especially for the visit to Safari Park. Parking costs $12 there. I think the train ride along the beach heading to Legoland is a tourist activity that will appeal to a child just as much as many other sights.