Using West's Annotated California Codes, what 1970 case states that a
city council's determination as to necessary condemnation of property
for an airport is conclusive?

It would be helpful to know the specific code section you are referring to.

Hello,

It is an eminent domain situation and whether the condemnation is "acceptable". 

Please reference below:

CALIFORNIA CONSTITUTION
ARTICLE 1  DECLARATION OF RIGHTS

SEC. 19.  Private property may be taken or damaged for public use
only when just compensation, ascertained by a jury unless waived, has
first been paid to, or into court for, the owner.  The Legislature
may provide for possession by the condemnor following commencement of
eminent domain proceedings upon deposit in court and prompt release
to the owner of money determined by the court to be the probable
amount of just compensation.