The 1/2 acre mark is attainable in Livermore for under $1,000,000 but you will only find one here... one there. Last year you couldn't find a home on a 1/2 acre lot in Livermore for under $1,000,000.
Your focus for this type of property should be in the Brentwood, Byron, Oakley area which is 17 miles east of Livermore. There you will find many more homes on larger lots and the homes are also much larger and they are also newer.
I was showing property yesterday in Livermore and Brentwood. In Livermore there were two homes on 1/2 acre lots under $1,000,000. The homes were @ 2,400 - 2,800 sq. ft., one built in 1997 and one built in 1963.
Just 20 minutes across Vasco Road there were 9 homes ranging in square feet from 2,800 to 3,800 sq. ft. They were newer homes (2 - 6 yeard old) and two of them were single story. Antioch also had a few homes with over 1/2 acre lot. There are also older ranch style homes in Brentwood, Antiock, Oakley and Bether Island under $1,00,000 on 1 - 5 acres if you are considering rural property. You can search the MLS for these homes at my website noted in Web References.
I hope this helps.