The Geography of Elfen Lied is centered around Kamakura, Japan, and many if not most places seen in the series are in fact real, some of the exceptions being two of the most prominent, Maple House and the Diclonius Research Institute, though a place like Maple House may exist, and there are islands off the coast. Reasoning out what falls where in the mix can be difficult.
Maple House and its possible real-world equivalent There are two major possibilities for the site of Maple House. One is near the Sasuke Inari Shrine and the other is near Jouju-in Temple/graveyard. Stone steps that the main characters often use when they enter and leave Maple House actually do exist on a narrow pathway that connects Sasuke Inari Shrine and Zeni Arai Benzaiten Shrine (between D and E of the first map). The Sasuke Inari Shrine, however, is located about thirty minutes away from the sea coast on foot. From the story's viewpoint, the more reasonable imaginary location seems to be in the vicinity of Jouju-in temple (B of the first map). Mamoru Kanbe, the anime's director, looks to have used the steps near Sasuke Inari Shrine as a representation of Maple House's fictional location, ignoring a more realistic placement near the Temple and Cemetery.
Nailing down the Institute
On the other hand, reasoning out the possible location of the Diclonius Research Institute is much more difficult. If a real-life version of the island actually exists, it would likely be in the Izu Chain, a group of more than 100 islands, including mere rocks too tiny to be called an island. (See Map Below) Between Miyakejima island and Hachijojima island, the strong ocean current that is called Kuroshio or Black Current starts from the north-east of the Pacific Ocean and reaches as far as the western coast of the North American continent, even carrying debris that distance as a result of the earthquake-induced tsunami in March 2011.
As Lucy was drifting to the shores of Yuigahama Beach when she escaped from the DRI, the possible candidates for the depicted island can be narrowed down to one of the islands located north of Miyakejima island. If the DRI island lies south of this Miyakejima island, such as near Hachijojima or even further south, then Lucy would have been cast ashore not to Yuigahama but to the currents leading to the North American continent, placing her survival in serious doubt. San Francisco, Los Angeles or any other cities on the west coast of the continent become places where a very different story could have developed.
The DRI's location most likely would be one of the uninhabited islands that lie north of Miyakejima island. Out of more than 100 islands and rocks in the Izu Chain, only nine are inhabited. There remain only eight major non-inhabited islands. They are a) Inamba-shima, b) Ohnohara-jima, c) Zenisu-jima, d) Onbase-jima, e) Hayashima, f) Jinai-shima, g) Utone -shima and h) Tadanae-jima. The photos of these eight islands are attached here. Out of the eight, only Utone-shima had inhabitants for quite a brief period in the 19th Century. The story states that the Kakuzawas and their ancestors had inhabited the island for centuries. It seems possible that, in the Elfen Lied universe, many of the various smaller islands of the Izu Chain were instead one landmass large enough to house a rather large facility with a deep underground grotto. It can be further speculated, based on stated story elements, that the radioactive nature of the grotto affected the distribution of the landmass in the Izu Chain.
Mayu's Railway Crossing
Perhaps an obviously symbolic place, an understandably suspicious Mayu takes Wanta and retreats from Maple House and Kouta and Yuka's offer of a place to stay. Recreated in the anime in the standard painstaking detail, we see and hear Mayu making excuses about why they shouldn't stay, to the point where it seems it's not Yuka and Kouta she suspects, but good fortune itself. Her hardly comfortable but now reliable existence rapidly implodes, as fate guides her back to be a core cast member. The crossing is a small one, off to the side, but like so many other small things, it gains power within the story, even if seen so very briefly.
Locations in and around Yuigahama Beach
Many businesses thrive and survive around this area. Also there is the spot one girl used as well, when she could no longer stay at home.
The city and town is not always the place we see in the series.
Photos and Maps of the island's possible locations
As stated above, these can only be used in a speculative sense. No island with the DRI's attributes exists in the real world. But these can prove useful in reasoning out a picture of where it would be in the world of Elfen Lied.