The island is not that big, To require overnight stays
You could drive the entire coast in a few hours

every village has numerous places with 'rooms to rent' signs outside,depends really what time of year you're there,for instance in august almost every single bed on the island is taken by greeks and italians and in resorts like Faliraki anything left over is almost always taken by english/polish/albanian workers whereas in may it's possible to just arrive at hundreds of places and have a room in minutes,Greece has very much got an informal culture when it comes to such things. In some of the more remote villages(of which few are actually 'remote')look out for hand painted signs saying 'ENOIKI DOMATIA',they're everywhere,often strapped to road signs or trees with an arrow pointing off to wherever the rooms are. Failing that just literally walk into any shop/taverna/bar and ask,99% of the time either they will have rooms themselves or their cousin/brother/sister/friend etc will have them,they're always prepared ready for arrivals and the rates depend on what you want.

The island is doable in a day or over 2 days with a return to your hotel but it is nice to get out,stay overnight in a village somewhere and then head off again in the morning,where you want to stay depends on what you want,personally i think it would be nicer to stay overnight in the mountains in a village such as embona,or aghios isodoros,particularly the former,there's loads of traditional tavernas up there and the village looks up into the vineyards on the slopes of mount attaviros,there's always loads going on in the evenings,you will see quite a few tourists up there who are staying overnight,many of them german or scandinavian but on the whole it's mostly locals that come in from the smaller mountain hamlets and farms for the night to see friends,have a few drinks or whatever and there's a really good atmosphere. loads and loads of good cheap local wine too! If you were to stay there and had the time and inclination then an early morning start and a trek around the slopes of the mountain is a good day for taking pictures and truly getting away from it all. Embona and other mountain villages are reachable on the main roads around the island and if you pass through Siana stop and buy a bottle of souma!

I buy a 5 litre bottle of souma for 25 € in a little distillery in Embona.You can buy small bottles these days in some supermarkets

Thank you for the information. Living on an island myself I realised that Rhodes could be done in a day but what sambacasua said regarding stopping over in the more remote areas is spot on.
I'm in Rhodes working for 5 days of the 14 days I'll be there so really was looking forward to driving up in 'them there hills' and kicking back for the odd night. If I wound up in the smallest of villages with just a bottle of beer, the stars above and a bed in a barn I'll be a happy man.

I do appreciate you both taking the time to answer so thank you very much. The idea of staying with a 'cousin/brother/sister/friend etc' of an establishment speaks volumes and I couldn't have asked for more. Sounds right up my street.

Thank you.