There are many options on where to stay when you arrive in Paxos. There are a couple of hotels and a big chunk of locals and foreigners who own properties in the island, choose to rent their cottages or villas during the summer months. Keep in mind that the majority of accommodation available is not recommended for the budget traveler.
Villas & Cottages
An independently run cottage or villa is the most widespread accommodation and your best option here in Paxos. You will find villas in any of the three main villages: Gaios, Loggos, Lakka, as well as in other areas of the island. Prices near the capital, Gaios, will usually be higher compared to accommodation further away. If you 
choose to book a villa not so close to the main hubs, you can get a good deal for it even if you have to book a car to get there too. Some sort of transportation is recommended anyway if you want to make the most out of the island, its best corners are well hidden.
You can find your Paxos home away from home by booking Monolitharo, the Paxos Traditional Cottage via email.
B&B
As with hotels, Bed and Breakfast accommodation is not widespread in Paxos. There are a few lodging options available but your best option is to book a local villa or cottage for the length of your stay in the island and arrange your own catering. There are plenty of restaurants (tavernas) in Paxos as well as mini-markets so eating out or finding fresh ingredients to cook will be easy.
Hotels
The island is quite small so it has been spared the construction of big hotels. There are a couple of nice hotels which you can opt for, however, the prices will definitely be higher compared to the independent cottages.
Luxury or Specialised accommodation
There are a number of specialised tourist offices that are able to offer luxury accommodation in the island and guarantee discretion, privacy, special facilities and services including ample space, swimming pools, sport courts, domestic help and much more.
A few examples of specialised travel agents are:
White key villas
Scott Williams
Simpson travel
Alternative travel
Paxos is a beautiful island, very green, with clean seas, plenty of hiking paths and many areas of an ecological interest, endless hectares of growing olive trees or vines. Naturally it has attracted the attention of ecotourism initiatives, alternative tourism and also younger budget travelers with an interest in a natural, unspoiled environment.
You will not find any organised camping facilities in the islands of Paxos or Antipaxos. Greek law actually forbids camping in public spaces in order to control fires, pollution etc. However, you will find quite a few tents in the main beaches of Antipaxos (Vrika and Mesovrika beaches), also near Loggos (Levrehio beach) and Lakka (Manadendri beach). If you do decide to camp independently, it is better to be near a restaurant, in order to have easy access to food, drinks and basic facilities.
Paxos travel agents
You can see a list of Paxos travel agents here.