There are 18 Siddhars 1)Nandhi 2)Agasthiyar 3) Thirumoolar 4)Ramadevar 5)Bogar 6)Konganar 7)Dhanvanthri 8)Vanmigar 9)Kamalamuni 10)Pathanjali 11)Sattaimunivar 12)Machamuni 13)Karuvurar 14)Pampatti 15)Korakkar 16)Kudambai 17)Sundarananthar 18) Idaikadar.
In the table below, the first number corresponds to the list in the picture above (an old official list) and the second number is the location on this map. Those names in blue letters do not belong to the official list of the 18 tamil siddhars. Nandidevar as seen on the official list above should be located in Thiruvaduthurai however I have not been able to locate it yet, the temple only contains the deity Nandidevar.

1) Agastiar Jeeva samadhi temple (Kumbeeswara-Temple)

2) Agapaei (Nayanaar) Siddhar - Not part of the 18 siddhars

3) Tirumoolar Jeeva samadhi temple (Masilamaneeswarar temple)

4) Sivavakkiyar / Nandi Devar
Masilamaneeswarar temple

5) Bhogar / Boganathar
Palani hill murugan temple - Jeeva samadhi of Bhogar siddhar

6) Kumbamuni - another name for Agathyar Siddhar
Sri Aadi Vinayakar (human faced Ganesh), Sri Kumbamuni Siddhar (Ganesh), Agathyar Siddhar

Sri Aadi Vinayakar (human faced Ganesh) // Sri Kumbamuni Siddhar (Ganesh) // Agathyar Siddhar
Image taken in a temple in Kumbakonam (Kutandai is the old name of Kumbakonam)

70. Agatthiyar the one within,

Translation:
You said you told us
Am I the child born for Kumbamuni?
You told me that you pacified, what will I do?
Siva sivā my guru Is it not to be mentioned?
His wisdom- what is its type
Is it silver or gold or is there something other than these two?
We praise you, My Guru!  The one who is within the heart
You will talk about this to Pulatthiyar.

Commentary:
This verse is Pulatthiyar’s part of the conversation.  He asks Agatthiyar whether he is Agatthiyar’s baby for him to pacify him.  He wonders about the nature of Konkanar’s wisdom.  He asks whether it is gold or silver or anything other than these two.  Silver and gold represent evolved states. 

7) Vamadevar / (Vanmeegar) Valmiki
Ettukudi Murugan Temple

8) Idaikadar
Back entrance of the Annamalaiar Temple - Thiruvanamalai

Back entrance of the temple, at the cow shed

Jeeva samadhi of Idaikadar near the cow shed

9) Sathaimuni / Sathainathar
Sattainathar jeeva samadhi temple in Thiruvedagam

The second jeeva samadhi of Sattainathar is located in the Ranganathaswamy Temple (Inside Goddess Ranganayaki temple. As you enter the entrance, turn right and go around the deity's main place.)

10) Kamalamuni / Kamala munivar
Thiyagarajar temple in Thiruvarur

11) Machamuni Siddhar
Jeeva samadhi on top of the Tiruparankundram hill in Madurai

12) Konganar / Konganavar
Jeeva samadhi - Thiruvaduthurai - 2 Km from Gomuteeswarar Temple

13) Pathanjali
Brahmapureeswara temple in Thirupattur, 30 km from Trichy

Jeeva samadhi

14) Pambatti
Sri Pambatti Siddhar Jeeva Samadhi Peetam, Sankaran Kovil

Arulmigu Subramaniyaswami Thirukovil, downstairs

15) Sundaranathar
Meenakshi Amman temple

Jeeva samadhi is located on the left corner from the signboard

16) Kuthambai
Periya Kovil Jeeva Samadhi - Mayiladuthurai

17) Karuvoorar
Pasupatheeswarar Temple - Karur

18) Goraknath / Korakkar
Goraknath jeeva samadhi temple north of Poigainallur

19) Thanvanthri
Jeeva samadhi

20) Pulathiyar Siddhar
Not part of the 18 Siddhars

21) Ramadevar (Yakub Siddhar)
The trail is behind Raakachi Amman temple, about 7 km trekking uphill to reach the jeeva samadhi of Ramadevar.

Alagar Malai jeeva samadhi

None of the pictures of the 18 siddhars come even close to how they really looked like and it is very difficult to find real drawings as most of them were destroyed by time or were never made. However some are available and they are mostly naked as that is how they were in real life. Below you find some examples.

Sattaimuni Siddhar (Sattainathar)

Sattaimuni Siddhar

Goraknath
Old Pratima, at Gorakhnath Temple, Odadar, Porbandar, Gujarat, India

Thirumoolar Siddhar