We will be in Mallorca in September, deciding where to base ourselves that isn't too crowded or full of tourist, for exploring, cycling and the beaches.

The west and northeast Tramuntana area of the island is extremely beautiful, but in September nowhere on the island will be void of tourists.
The villages of Sóller, Port d Sóller, Deiá, Pollença, Port de Pollença, Valldemossa are my favorites there and extremely photogenic. For easy beach access, Port de Sóller and Port de Pollença.

Thank you, We are deciding between those exact towns, Do you have feedback on choosing between Valldemossa, Pollenca and Soller as a base? Bike shop, hiking, beach exploring are important to us.

Yes, I visited them all but used Sóller as a base and stayed in a former citrus merchant´s mansion. But if beach is important to you, I would stay in Port de Sóller at the beach or in Port Pollença, where there is a more expansive beach. Hiking and biking and exploring....everywhere.

Thank you again Maribel. We are leaning toward Soller or near Valldemossa. are the accommodations in the former citrus merchants mansion one you recommend?

Yes, but remember that for the beach you'll need to take the ancient wooden train-tram from Sóller down to Port de Sóller. The ride is a treat, but in Sóller you won´t have the beach at your footsteps. Our host was an avid cyclist. This is serious cycling country!

Please if possible share the name of accomadation you were happy with , or the cyclist,
Thank you

This is where we stayed in Sóller and the manager is the cyclist.
The Salvia
https://www.hotelsalvia.com

The Garden Junior Suite is my favorite room.

I must be geographically challenged today. In post #2 I meant to say the west and northwest of Mallorca are the areas we found most interesting and beautiful---the Tramuntana.

Maribel,
Thank you very much for the information. Do you have any recommendations on where to stay in Madrid? We will be there for only two days at the end of our trip before we fly back to the states.

Maribel and I share a love of great and interesting accommodations.
Just a quick comment about Hotel Salvia. If renting a car Hotel Salvia doesn't have on site parking facilities. We were in Sóller August 2022 during one of their major festivals. Driving in and out of town and parking were major challenges.

My personal preference is for Pollenca town, about 5kms inland from Port de Pollenca. As Maribel knows, this is my go to place on the island, for its Catalan feel, restaurants and lovely village centre. The Hotel Son Sant Jordi is excellent, nice rooms and pool and a two minute walk into the centre. Pollenca has a number of good restaurants too all around the main square and in the side streets.. The port is a 10 minute car ride away and has a great beach hat stretches almost to Alcudia, but it always feels good to get back to Pollenca town for the evening.