Baku 
Gyanja 
Naxcivan 
Nakhchivan is a little visited enclave of Azerbaijan, seperated from the 'mainland' part of the country. This is one of the less frequented by tourists part of the world. You
would hardly meet here any foreigners/tourists apart from Turks and
Iranians.
The most common way to reach Nakhchivan is via air from Baku. A new route has started operating from Istanbul recently, and it might be even cheaper for those travelers who come from Turkey. There is a border point near Idgir (Turkey). You can take a taxi from there (would cost you around $30-40) that will take you to Turkish-Azeri border.
You can reach Nakhchivan through the Turkish corridor between Armenia and Iran - there is a 10 km border between Nakhchivan and Turkey.
Noah's grave. Beautiful monument with photos and paintings inside the monument. The story says that the grave was at this place since it was one of the highest points of the city. A local painter painted the grave in the early nineteen hundreds and it was then rediscovered later and the upper part of the monument was added.
Another suggestion is to visit The salt mines located 10 km outside the city. This is actually an asthma centre drilled into the salt mountain. It is used for asthmatics as a natural cure: the clients sleep inside the cave during the night. The smell of salt is very pervasive as soon as you get inside. There is a long path to the 'hotel' inside. You will definitely find it interesting. o enter the mountain, one needs to get approved by a doctor, but they generally don't mind. There is also a newly build 5-star hotel just outside for the relatives of patients that spend nights inside salt mountain.
Ashabu Kahf are quite beautiful mountains with interesting caves. People come here as they believe this is religious pilgrimage sites. It is not specifically Muslim, but emanates from a legend where some people slept for 309 years in these caves, while a tyrant ruled. The story is somehow mentioned in the Koran Ц the story about the Seven Sleepers. It has been a pilgrimage site since the 6th century.
Snake Mountain (Ilandag, 2415 m) is a photogenic mountain that sticks up from the plains. A local legend says that the cleft on the top was made by Noah's Ark.
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