I arrive in Madrid on 4/25 at 8:20 a.m. after an overnight flight from the U.S. I leave Madrid on 5/16. I am traveling solo for the first time and trying to plan my route in the most time efficient way to see the most I can without killing myself and everything becoming a blur. LOL I want to use public transportation rather than rent a car, if possible. I want to find a central location to stay in for a few days at a time so I don't have to move around so often; therefore, take day trips for as many sightseeing trips as possible. I am interested in history, archaeology, architecture, art, gardens but not so much food and wine. I know I want to see Madrid, San Lorenzo de El Escorial, Segovia, Toledo, Granada, Cordoba, Seville, Ronda and the White Villages, Jerez, Cadiz, Costa del Sol (Malaga, Torremolinos, Marbella, Estepona), Portugal's Algarve. I have to visit my friend that moved last year from the U.S. to Alicante for 2-3 days during this trip and we might go on a day trip to Valencia. I don't know where Alicante fits in the schedule of seeing the other cities. In addition to all this sightseeing and visiting my friend, I'm keeping my eye open for places that I might consider moving to permanently (maybe Portugal more than Spain because of income taxes) so would appreciate opinions about cities/towns that aren't too small (at least 50,000 people) with some cultural activities, decent shopping, close to transportation, a nice walkable downtown area and not having a car is okay. I am 65 this year, divorced and currently live in suburbia outside the Houston, TX metro area and while it's an affluent area with much cultural activities, restaurants and shopping I don't enjoy the traffic, the crowds, the horrible humidity and torrential rain, the go go go pace.
I figure at least the first 3 days in Madrid. Day 1 of arrival probably do the Hop on Hop off bus tour to get an overview. Maybe go to El Retiro Park. Day 2 Tour Royal Palace, Prado Musuem, Reina Sofia Art Musuem, Thyssen-Bornemisza Art Musuem; Day 3 Trip to El Escorial and Segovia (buy a guided tour for this trip); Day 4 Train to Toledo. This is as far as I can figure out what I'm doing. Do I stay in Toledo overnight or go to Granada for the night or go back to Madrid????
I know this is a lengthy post but I wanted to give as much information as possible with the hope that any advice received will understand what I'm trying to accomplish. Thank you in advance.