There's lots of great info about Oakland's street trees here.
The big oak in Frank Ogawa Plaza in front of City Hall is called the Jack London Oak.
If you want to see lots of trees, check out some of Oakland's natural spaces.
Here are all the pages about trees on this wiki:
If you want a huge, slow-loading map of all of Oakland's trees, you can get that here: http://mapgis.oaklandnet.com/Trees/ (the CSV source file for that is here).
Here are some better maps of trees, broken up by neighborhood:
You can download the geojson too if that is your kind of thing.