The three lakes you can fish in is Geitabergsvatn, Þórisstaðavatn and Eyrarvatn. They are all part of a water system including the salmon riveer Laxá í Leirarsveit. Salmon can be cought in the lakes. Lake Þórisstaðavatn is biggest of those three, 1.37 km2 and it rises 71 m above sea level. Greatest deepth of that lake is 27 m.
You can choose from three lakes in Svínadal in Hvalfjarðarsveit. Distance from Reykjavík is about 82 km if you go through the tunnel under the Hvalfjord. The lakes are about 27 km from the town Akranes. For inhabitant from Reykjavik it it a brilliant idea to skip the tunnel (on highway 1) and drive the Hvalfjorður, that has a spectacular view. That road only takes 15 minutes more. Fishing is allowed in all lake Þórisstaðavatn and Geitabergsvatn but only the north part of lake Eyrarvatn. Please note that it is forbidden to fish close to the rivers. There is a nice organised camping area at the farm Þórisstaðir where you can buy access to. You can also rent summerhouse and a trailer there.