I have also travelled alone thru europe before, the biggest piece of advice I can give you is to stay in HOSTELS. That is the best place to meet people and have people to hang out with for a couple of days. You will become lonely travelling by yourself and the hostels are a great way to curve that.
madrid def warrants a day trip to toledo... for sure... depending on ur budget, take the train, but if youre really tightt take the bus, its dead cheap, just takes a while! well, 2 hours or something.
if ur based in the UK then i wholeheartedly agree with t_maia. whats the hurry? do a few countries then go home, save up and do it again... you have the benefit of budget airlines and being really close to the mainland. if youve never been alone overseas then it would benefit you to do one trip, come home and learn from it, then do another one at a later date - i think everyone at some stage needs to learn to travel!