There are not many castles in Middle Earth. Tolkien used towers as places of military strength, and of these there were many. Try doing a search on "Towers".
As for the second part of your question, there are also many "Elven places" in Middle Earth. In the Third Age, the chief abodes of the Elves were Imladris, Lothlorien and Mirkwood.
In the First Age there were too many places to name. Aside from the Undying Lands, there was the Kingdom of Thingol and Melian that is called Doriath, along with Hithlum, Dorthonion, Nevrast, Thargelion, Himlad and Dor-lomin, which were the abodes of various Noldorin Elves (Fingolfin, Fingon, the Sons of Feanor, etc.). These were all part of or in the general vicinity of Beleriand, the large land area wherein the battles between the Elves and Morgoths took place, I am just writing these off the topic of my head, since I do not have the
Silm with me at the moment.
Cirdan the Shipwright was Lord of a place called the Falas during the First Age, and later he abode in the Elven realm of Lindon in the Second Age. In much of the Third Age and into the Fourth Age, he dwelt at Mithlond, the Grey Havens, and his ships sailed away with Elves to Valinar before, during and after the War of the Ring.
This is really just a random collection of thoughts. You can learn more about any of these terms via a search on these fora, a look at the
Encyclopedia of Arda or any number of other sources.
Cheers,
Angmar