Where to stay in Portugal

When are you travelling?

Do you want just one base or a tour?

Yes, hiring a car is easy in Portugal.

The Algarve is good for beaches, but is filling up rapidly for the summer months. There is Lagos Zoo (a few miles out of Lagos and there are a number of water parks across the Algarve. Alvor is good for families. The Meia Praia area of Lagos has level access. Many Algarve beaches are accessed via lots of steps from the cliff tops.

The Algarve isn’t known for its museums - Lisbon would be better for culture.

With Lisbon as a base, you would have access to beaches within a 30 minute train ride, and would have the zoo, aquarium, parks, etc. With Lisbon as a base, you would not need to rent a car.
Porto also has beaches close by.
If you just want beaches, the Algarve will give you a better variety and you would need a car.
I would encourage you to read a guide book - RS, Lonely Planet or others to give yourself some basic information. Then you can see which each area has and what appeals to you.

Where can I purchase this book? Perhaps I wasn't clear. I want to plan the whole trip (every day) right now, and planning in July 2018. This includes places to stay and tours, just don't want to plan on sight. And yes 30 m from the beach is too far with a child, maybe I should look into beach resorts (but definitely interested to show my son another culture, Museums, expose him to history) so I'm not the one to just lounge. But limited in how much my son can take, we did Mexico and it was hard for me cause I didn't make it in time for all the excursions I booked, which caused a river of tears. I now know not to schedule more than 1 excursion per day (trust me, children are much slower travelers than us) but take it easy.

You can purchase a Rick Steves or Lonely Planet from any bookstore or order on Amazon.
And, planning most everything before you arrive is a good idea.
I would not encourage a resort as it keeps you away from the real Portugal.