The bus/subway metro tickets are a good use, no matter where you might be in Madrid. In fact, I usually have one or two rides left on them when I leave and save them for the next visit. Some of the larger stops have personnel there to dispense them for you. Otherwise, you will easily find someone to assist.

Not sure about the area you are mentioning, so can not comment on it. But Madrid I know you will certainly enjoy! At the Palace be sure to see the armory..most people I believe go right by it, but it is fantastic. You can walk to most of the places in the city that you will want to see, so wear comfortable shoes.