It's only the express trains whose tickets vary in cost. Alcala de Henares is served by Cercanias trains from Atocha Station; some also stop at Chamartin. No assigned seats, no sell-outs, so you can just buy the ticket when you want to travel. These trains are heavily used by commuters, so I imagine the schedule is less frequent on Saturdays and especially on Sundays. There are two stations in Alcala. I think perhaps the University Station may be more convenient to the historic center.
Note: I don't know whether the rule applies to Cercanias trains, but regular train tickets cannot be sold less than 5 minutes before departure. Don't cut it too close.
Toledo is an exception to the varying-prices-on-express-trains rule; the fare to Toledo doesn't vary. But trains to and from Toledo can sell out, so it's not a good idea to plan to buy that ticket right before you hop on the train. At the very least, you should monitor ticket availability on the Renfe website (or I guess use the app--but I've never done that). The website, at least, doesn't tell you how many tickets remain, but trains that are full will be so labeled, so when the first trains is marked "Full", that's a warning that you may not be safe to wait. In a pinch, there is also bus service, but it is a lot slower. I love Toledo and think spending a night or two there is a fine idea.
For Segovia and Salamanca, there are potentially really substantial savings from buying tickets early for the fast trains. Alternatively, one can take a slower train, but it will take much, much longer. Take a look at the schedules and fares to Segovia on Renfe.com to see what I mean.
Do not under any circumstances get yourself in the position of having to use the staffed counters selling long-distance tickets at Atocha Station. The lines always seem to be horrendous--as in hours long, and a lot of the people in those long lines have tricky purchases to make that will be very time-consuming. Buy your tickets on the website, in the app, or from a ticket machine. I assume they still have different machines for different types of tickets/destinations, but once you find the right machine, it's not hard to buy the ticket. There may be uniformed Renfe employees floating around the ticket lobby; they can point you to the right machine for your trip.