I've read both the Silmarillion and Lord of the Rings. Both take place in the 'west' of Arda, and Beleriand (where most of the Silmarillion takes place) is destroyed. So where is the Middle-Earth of LotR? Does anything from the Silmarillion take place there? Can we point to places on the map that exist in both epics?
I was about to answer in depth, but then an image search showed me an existing answer online, though there's quite a bit of extraneous text there. I'll borrow the maps from that blog:
This is a map of Beleriand, in the first age. Conveniently, the Blue Mountains are circled:
And now a map of Middle Earth in the third age:
These are the same Ered Luin, Blue mountains. Beleriand, before it sank into the sea, was westwards of where the Shire is in the Third Age.
To supplement Anver's answer, here is another map, sourced from History of Middle Earth 7 (The Treason of Isengard), which contains an extended account of the first LotR map:
This was drawn by CT from one of JRRT's working maps so it may be considered an accurate representation.
Here, the island of Himling corresponds to the hill of Himring in Beleriand, and Tol Fuin with the highlands of Dorthonion/Taur-nu-Fuin. To quote from CT's note regarding the Unfinished Tales redrawing:
Although Christopher Tolkien notes that "the fact is nowhere referred to", it actually is; in HoME 7 (Treason of Isengard), Chapter 6 (Council of Elrond (1)) text of "a single sheet of manuscript found in isolation" reads (in part):
CT confirms in a footnote that this "single sheet" was only discovered after he had written the Unfinished Tales note; hence his original statement (now known to be incorrect).
The river in Lindon may be the remnants of the Gelion, and what's especially interesting is that if you examine the Beleriand map in the Silmarillion, you'll see that the westward protrusions of Ered Luin there (in the area of Mount Rerir/Lake Helevorn) correspond in shape to the same area in the map above (to the east of Himling).
Also interesting is a hint of the location of Utumno, in Return of the King (note 25 to Appendix A, discussing "the Lossoth, the Snowmen of Forochel"):
From this it may be inferred that the remnants of Utumno are under the Icebay of Forochel, giving you another correspondance between the LotR maps and the tales of the Silmarillion.
In the Silmarillion we also read that after the Battle of the Powers (which resulted in the first Chaining of Melkor):
This seems to indicate that the Great Gulf is the Bay of Belfalas, assuming that it's size in the First Age was comparable to it's size in the Third.
The Great March of the Eldar also passes through some well-known locations:
And also of the wanderings of the Nandor:
And finally, RotK Appendix A discusses the origins of the Barrow-downs and their relationship to the First Age:
And to supplement their answers, a map from the LotR Wikia:
The fully drawn bit is (the north-west corner of) Middle-earth in the Third Age, the faintly drawn part is Beleriand. Again you can see Tol Fuin and Himring/Himling.
EDIT: Jimmy Shelter commented (quite rightly):