Here are some things that are my favorite ones on Thasos, and I recommend you try them.
1. Moussaka
2. Stifado
3. Pastitsio
4. Kleftiko 

Stifado is a traditional dish with rabbit meat and when you order, specify that you want it with rabbit meat because it can be prepared with veal also. Both are delicious. This meal is prepared in ceramic dish in combination with very small onion bulbs.

When it comes to homemade Greek dishes, then you should certainly try Greek moussaka.

Pastitsio is similar to lasagna. Pasta with minced meat.

Kleftiko is my favourite dish. very delicious meal with lamb and vegetables in a ceramic dish. The best one I tried in a restaurant Piatsa Mihalis in Potos and one serving costs 13 euros but it's worth it. I recommend that you try it in that restaurant! Another good place for kleftiko is in the restaurant Mesogios in Limenas.

In Poseidon restaurant you should definitely try chicken fillet a la creme with mushrooms!

When it comes to salads or appetizers you should try:

  1. Bouyiourdi
  2. Tirokroketes
  3. Halumi

Bouyiourdi is mix of cheeses and tomato, warmed up in a clay pot. It's prepared differently and the best one for me is in the restaurant Irene in Potos.
Tirokroketes are something like fried cheddar cheese balls, and halloumi is a special type of cheese which you can fry on barbecue.

I recommend fish eggs salad for those who like stronger flavors. It’s called tarama.

Octopus is usually ordered as an appetizer and can be prepared in several ways. The softest is when prepared in wine (krasato) while on barbecue can be stiff especially if it's fresh.

Of course, make sure you try tzatziki. It is a salad that mainly consists of sour crème, pickles, dill, garlic.

I recommend you the following sea food:
1. sea food risotto - the best one for me is in tavern Limani in Limenaria
2. Yellow sauce clams - the best ones in tavern Armeno in Skala Maries
3. Shrimps in any way (grilled, cooked, or in sauce)

1. Fagri
2. Lavraki
3. Lithrini

and from smaller fishes barbounia.

1. Whole nuts in pine honey (can be bought in all shops)
2. Kataifi
3. Trigono (the most famous sweet of Thessaloniki and Northern Greece. It is triangularly shaped, and reminds of baklava filled with white cream)
4. Baklava with pistachios