I spent 3 nights in Toledo and was very glad to have two full days there plus a few extra hours. It is a full-day destination as far as I am concerned. Train from Atocha Station. Then you can take a bus up to the historic area. It's walkable (there are escalators to assist), but that takes quite a bit of time, and believe me, there is tons to see in Toledo. On foot; the streets--such as they are--are medieval, twisty and narrow. Most of the historic area is pedestrianized; be warned that parts of it are rather hilly.
Rail fares to Toledo do not increase as your travel date approaches, so there is no financial reason to buy tickets now. There is a theoretical possibility (perhaps not so theoretical on a weekend or holiday) that a train might sell out, and Rick specifically warns about that problem on trains going back to Madrid in the evening. The other potential issue is that Atocha Station is a bit of a zoo; you shouldn't show up 15 minutes before train departure time planning to buy your ticket and run for the platform.
There is some fare variation on the trips to Segovia, so you may save some money by buying that ticket earlier. Otherwise, I don't think there's a rush to buy tickets. I believe there is a bit of a walk from the Segovia train station to the historic area. The latter is not so large as to be an issue for folks with normal mobility, but transportation to the edge of the historic area in the form of a taxi (unless buses are available?) might be worth considering. I liked the walk very much for the introduction it gave to the aqueduct. Allow time to see the rest of the old town; it's quite picturesque. You don't need as much time in Segovia as in Toledo, but it's still worth a full day if you can spare it. I think Segovia is known for suckling pig, so you might want to plan a special lunch there if you eat pork.
Note: In Spain a round-trip ticket (ida y vuelta) is sometimes about the same price as a one-way ticket, so it's worth checking RT fares very carefully before you buy anything. For Toledo, I encourage you to plan a late return to Madrid, because I think you'll be happy to wander around the upper town even after the sights close. There can also be a wait to get into the cathedral; you may need to buy your ticket and return later to go inside.
Cordoba is about two hours away (it's more often suggested as a day-trip from Seville if not as an overnight stop) and may be painfully expensive for a day-trip if you do not pre-purchase your AVE tickets. Go to renfe.com and check fares for tomorrow to see what I mean. BUT I see that round-trip tickets are in some cases cheaper than one way. I do not know that the situation will be the same in May, but it looks good at this point.
Edited to add: I haven't been to Cordoba recently, but in my experience, any European city of reasonable size has transportation from the train station to the historic area if distance is any sort of issue. And if you don't want to wait for a bus, there are nearly always taxis available outside the train station.
All three are great options.