With no motor boats allowed, Lexington Reservoir seems like a nice way to spend an afternoon. It's not a big lake, only 2 miles end to end, but it has several offshoots to explore. The Miller day use area is accessible by boat or car and in only 1/2 mile away from the boat ramp. It has picnic tables and a porta potty.
There is a $5 lake use fee, $6 parking and $7 boat inspection fee.
Here are some pictures of Lexington Reservoir:
Here is a description of Lexington Reservoir from the Santa Clara Parks department:
Here is a park map:
This is the location of the boat launch on Google Maps, which you can use to get directions to: