I am currently in Portugal. We traveled to Lisbon with a day trip each to Belem & Sintra, then on to Porto with a day trip to Guarmeres, then we traveled to Madeira and are now in the Azores (Sao Miguel). My family's experience has been that everywhere we've gone has been incredibly hilly. This cannot be understated. Bring your best sneakers for walking with a good grip on the soles. The sidewalks everywhere have mosaic tiles and can be a bit slippery too. There is no need for dress shoes in Portugal, in my opinion, after all this climbing and walking. I am currently in the Azores on Sao Miguel, and where we are staying in Ponta Delgada has been some of the flatter terrains we've had our entire trip.
I was worried about the hills coming to Portugal, so had been upping my workouts so I could handle all the walking uphill. Still, it was not enough. My husband, children (both 16), and I are not out of shape, but the seemingly never-ending uphill walks followed by steep downhills get tiring. Yes, there are some escalator/elevator things, but they may not always be convenient, and you really can't totally avoid the hills. I'm just being honest about what I experienced. Add to this the heat you might experience when you are going, which could be very draining. I would suggest maybe lining up some door-to-door transportation (you won't want to drive in Lisbon) for certain things. For Sintra, even taking public transportation once you arrive at the Morrish Castle and Pena Palace, you will still have an uphill climb. We did not go to Lagos, so maybe that is less hilly, but I'm not sure.
As for the hospital, about 10 years ago my late father-in-law was on a cruise and docked in Madeira when he needed to have surgery there on the island. He had surgery there and all went well and it was a good experience medical care wise.