There are many different opinions on this subject. Here is mine.

Limenas: the capital city and the biggest one, naturally has the widest range on stores, cafes, restaurants, banks, rent-a-car agencies, doctors consulting-rooms... The city beach is not bad, and the closest ones that are better are Paradise beach (15km), Makriamos (2km), The Marble beach (6km), Pahis beach (10km), Golden beach, the village of Pagania... The ferry-boat docks at Limenas, so there’s no need for extra traveling to the south part of the island, that is Limenas and Potos (another 45-50km). So if you want a quiet summer holiday, Limenas is the one offering the most, although since the port and the beach are not exactly in the center of the city, Limenas is not like cities on Halkidiki where the beach occupies the central part and where you are able to, no matter where you are located, get to the beach and back within minutes. When choosing your accommodation, you should also pay attention to the fact that, the distance from the see is not the same as the distance from the beach. The beach located near the docks is practically unusable, since it is full of rocks and sea urchins. I see that many agencies offer accommodation in that very part and that on their sites they say that the accommodation they are offering is within 200m from the beach or 2 minutes on foot. Therefore, if the beach is of priority to you because of the children or any other reason you might have, choose accommodation in the vicinity of the old port, not the new one.
Of course, it would be a shame to spend all of your days bathing at the beach in Limenas. That way you wouldn’t be able to see the color and clarity of water, for which Thasos is well known.

The advantage of staying in the south part of the island is the small distance between Potos and Limenaria, so you can easily exploit the benefits of both.

Limenaria: this is an ideal place for those who want to rest themselves before anything else. There is never any crowdedness in Limenaria. There is a relatively large walk by the sea. The beach in Limenaria is nothing special, but as I have already mentioned, because of the problems with getting into the water, but on the other side it is so long that you can be apart from others up to 50m if you want to.

I will spend some more time on the topic of the beach in Limenaria, since it is one of the most argued things when it comes to Limenaria. Even though most of the people are not so sure about the beach in Limenaria, I don’t think the matters are so grim.
People who choose Limenaria have three possibilities when it comes to swimming. The first one is the small city beach. It is located in the center of the city, and although it is tiny, it is quite decent. One part of that beach is sandy, with a gradual entry into the water.

The other possibility is the beach which is on the right of the center of the city, at the end of the walk. This beach is 2 km long, and sandy on the beach, but the entry into the water is quite rocky. Since the beach is long, you can walk along it and find a better entry point into the water. There is a well-known sandy entry point in front of the Grand Beach Hotel, which is about a kilometer from the beginning of the beach.

I have met lots of people who are not bothered by the rocky bottom, since they swim in the water and not walk through it, and like the beach because it does not have a shoal.
Well, I’m one of those who are bothered by the rocky bottoms, and I rarely swim in places which have them, so I’m not a big fan of Limenaria beach, but I am at it most often since it is closest to me. I have lengthened this description, and what I wanted to say is - if you are a fan of long sandy beaches and want one of those near your accommodation, don't look for accommodation in Limenaria.

So, both the small city beach and the long beach are quite usable and can be used in breaks between two tours. The problem starts when it rains and the water from the surrounding mountains starts pouring down into the sea. That is when water becomes brown and it is very unpleasant to swim in it. The turbidity doesn’t usually last for long, but when it comes to the weather, you never know for sure.

The third option for swimming in Limenaria is the Metalia beach. It's located behind the hill with the Palataki on it. It takes about 20 minutes on foot from the center of Limenaria to get there. The number of minutes depends on your physical condition, because, in order to get there you have to climb up the hill and then go down the hill, which can take a lot of time if you're not very agile or if you are with children. This beach is certainly not suitable for children, due to large slippery slabs, but it is ideal for those who search for some peace and quiet, clear water and swimming. The beach itself is situated on a beautiful place, surrounded by pines (there is no natural shade on the beach itself), ideal for relaxing while reading a good book.

If the beach is the biggest disadvantage of Limenaria, then its advantage is there are never any big crowds in the city itself or at the beach. Limenaria has a very big promenade, especially compared to Potos, a great number of restaurants where you can peacefully enjoy your meal while listening to some soft music, which is not the case with Potos, where restaurants are situated by the coast, close to noisy cafes.

Potos: if you are a fan of fair-like atmosphere, then Potos is the place for you. The fair-like atmosphere includes: crowds, noise, liveliness, crowded restaurants and cafes, loud music... The beach is better than the one in Limenaria. It’s mostly sandy, with a sandy and gradual entry into the water. Potos is ideal for the fans of a static holiday, since it offers everything needed for a fine holiday, without the need to leave to other places. The advantages of Potos are the closeness of Pefkaria (less than 1km), the closeness of one of the most beautiful beaches on Thasos, Psiliamos (4km), sandy beaches: San Antonio (the extension of the city beach), Notos is 2km away from Potos and so is Roso Gremos. Teologos is 10km away. There are restaurants and cafes by the coast which are quite nice. The disadvantage of Potos is that it has a promenade so short, that if it were any shorter there wouldn't be one. Another disadvantage could be that restaurants and cafes are practically joined together, so you hear loud music no matter where you are, out for a drink or out for a meal.