Region de Murcia

Forgot to say we will be traveling by car, thanks

While you didn’t care for it, we enjoyed Mojacar for the one day we were there. We stayed at the Parador. I haven’t driven the coast north of Cartagena for years, so have no idea what’s there now. When we drove the area from Motril to Murcia city in September a few years ago, we found many of the smaller towns had pretty much shut down for the season, so little was open. Hopefully Nick will chime in.

Hi,
I spent quite a few summer holidays just east of Águilas. If you like Cabo de Gata, you might like the stretch of coast between Águilas and Cartagena. Bolnuevo beach is big and pleasant, though developed. The coves west of Calnegre are also beautiful, but can be rough for swimming - my memories are hazy.
Never been to Isla Plana itself but it looks well located for the places I mention, and not too develop.
As for La Manga... It is a sad sight. What must have been a place of significant natural beauty has been utterly over developed. You can stay away. Only upside is the warm, shallow, calm water of the Laguna (inland side of the spit).

Mar Menor would suit your swimming preferences, but I'd certainly avoid the built up La Manga (think Rimini). However there are more peaceful places on the inland side, such as Los Urrutias. But all this area is fairly touristy (not so busy on the beach by October, though, and its a little south of the golf-central part) plus ex-pats. None of this area, or indeed anywhere else, is going to be a hidden gem untouched by tourists and ex-pats.

Staying south east, would put you near Calblanque natural park which is good for walking and has beaches (possibly deserted in October). It's perhaps the closest equivalent to Cabo de Gata in Almeria. I don't know if there are any official campsites in this corner, or what else for accommodation is available, but it would be worth visiting for some days (only about 15 minutes drive from Los Nietos on Mar Menor for example).

I've never been to Guardamar del Segura or around. Strictly speaking its in Valencia rather than Murcia (I think). That doesn't matter, except as you say it means longer drives to visit the "deep south". Cartagena would an hour's drive each way, plus city traffic/parking. Coastal places either east or west of Cartagena would be longer still.

Have you visited Anteqeuera in Andalucia? If you liked that, you might also like Lorca. They're similar in being inland, low-key, a few sights, including a castle on a hill, and generally sleepy out of season. Perhaps worth a day-trip from wherever you end up staying.

I can understand it doesn't fit with your plan for a single base. But I'd highly recommend considering if you can have at least one night staying in Murcia city centre. Whilst the city is never going to "beat" Sevilla in tourist attraction terms, it does really come alive in the small centre during evening paseo. It's a foody capital these days and a great place for a tapas bar crawl and late meal. Because the central area is fairly small, it's a university city and has lots if families too, plus it's not a major tourist destination, I think it has one of the most atmospheric evenings out in Spain.

Finally, Isla Plana. I'm biased because it's where we chose to live when I was sent here for work. The project I'm working on is nearly finished and we'll return to England next year. I think we felt we made a good choice being here. It can be busy in the Summer, and we're not the only British ex-pats by any means. But it's pleasant, convenient for visiting elsewhere in Murcia, has walking options (e.g. Sierra de la Muela). As for the main beaches, some info below. It's not quite as calm as Mar Menor or the coast further round in the Med, towards Valencia, but not noticeably stormy either.

https://murciatoday.com/cartagena-beaches-playa-isla-plana_31364-a.html

Thanks to Balso for your ideas, I will have a look at Calnegre too :)
Thanks Nick for taking the time with your long and very useful message. I hadn't thought about Lorca and will definitely add it to our list, yes we visited Antequera and liked it.
I will also bear in mind what you say about Murcia in the evening, we will stay a night somewhere when driving back up at the end of the trip.
I also feel much more convinced about Isla Plana now I know you chose to live there! I will have a look at Sierra de la Muela too. In Isla I found camping Los Madriles and reviews seem positive. Thanks again for your help and best regards.