Madrid with a 77 year old

There are pedicabs taking tourists around historic areas of some cities. I've never used one, and I don't know how the price compares to a taxi.

Most major cities have one or more city buses that run past several local sights, though not necessarily through the heart of the historic center. Rick's good about mentioning that sort of thing. If you don't already have his guide to Spain (assuming your trip isn't limited to Madrid and surroundings), you should buy it.

With Segovia the two main sites are the Alcázar and the Roman aqueduct that crosses the historic center. Since vehicles have been unable to drive between its arches since about 1979, by necessity busses must go around the center. Because of the hills, any bus coming down the one hill must go by the base of the aqueduct before going back up hill to the Alcázar. The historic center is pretty compact. My guess is a taxi would be very inexpensive since the Alcázar is 1 mile from the aqueduct and historic center. To get a good view of the Alcázar, go to one of the overlooks, Mirador del Último Pino or Mirador del Alcázar y los dos Valles.

For a regional specialty visit the Mesón De Cándido by the base of the aqueduct. It’s famous for its cochinillo; 21 day old roast suckling pig. If you’d rather try it in Madrid, visit Sobrino de Botín, the oldest restaurant in the world in continuous operation. Artist Francisco de Goya worked there for a while.

I’ve never taken a hop on-hop off bus, so can’t help with them in either Segovia or Madrid. If you think she may tire of a museum in an hour, consider the Prado and Reina Sofía free admission hours. That would save you some money too.

Prado Free entry from Monday to Saturday between 6 PM to 8 PM and Sundays and public holidays from 5 PM to 7 PM.

Reina Sofía free hours: Monday 7:00 - 9:00 p.m., Wednesday-Saturday 7:00 - 9:00 p.m., Sunday 12:30 - 2:30 p.m.
HolidaysApril 18, May 18, October 12 and December 6

The free museum hours are a very good idea.

Check museum websites ahead of time to see whether there's a cafe or restaurant. A food break is a great opportunity to rest tired backs and feet. See where the food source is located and the hours it is open and factor that into your plan of attack. There can be a great deal of walking required to move around a large museum, and the ceilings are usually high, so there are likely to be many steps required just to ascend or descend one floor. There will nearly always be an elevator available for those who need it, but getting to it may require extra walking.

It would probably be helpful to print out a floor plan and take it with you. Some museums stopped providing them during COVID and haven't resumed. Some folks are comfortable taking a picture of the posted floor layout.

Edited to add: I've seen lightweight, folding stools in some museums (not in every room), and some museums have wheelchairs available. I wouldn't broach the latter subject initially, because MIL might be offended, but perhaps if she struggles. I don't know whether the wheelchairs have to be reserved in advance.

Perhaps you could involve her more in the planning so that she will have some specifics for her must-sees -- especially if it's a bucket list trip for her. It's really hard for you to try to plan in a vacuum.

You could start that process right away by pointing her to the information about travel in Spain in general here on the RS website: https://www.ricksteves.com/europe/spain

And on Madrid in particular: https://www.ricksteves.com/europe/spain/madrid

Both of those links provide access to other useful information like videos to watch as well as to the relevant RS guidebooks.

Assuming she hasn't been to Europe before, she'd also probably benefit from reading the information covered in the Travel Tips: https://www.ricksteves.com/travel-tips
Those sections are great for helping to learn what we didn’t know we needed to know.

It's been my observation that the biggest cultural shock about traveling in Spain is the significant differences in mealtimes and what's typically eaten when. Sometimes it's worth it to stay in a business hotel that lacks charm, but has an elevator and a fabulous breakfast buffet. You also might consider renting an apartment if you're going to be in Madrid for awhile. It could be cheaper than getting 2 rooms.

Apartment or hotel room, make sure that the 2nd bed is a real bed and not a sleeper sofa. I'm 77 myself and fairly active, but I need a real bed, even if it's a twin.