Books

To use Rick Steves books for these places, you will have to buy at least two books. Budapest and Bratislava are in his Budapest Guidebook. Vienna and Melk are in his Vienna, Salzburg & Tirol Guidebook.
Budapest, Bratislava, and Vienna are also in his Eastern Europe Guidebook. Linz does not appear to be in any of his books. In your situation, I'd try to get an Austria guidebook out of the library, and just copy the part about Linz, since you'll only be there for a day. I'd then buy the Rick Steves books, and cut out the relevant sections; bring these, and leave the rest of the books at home.

You might try to find Bradt guides or Rough Guides, or Lonely Planet guides. They all cover where you want to go, but one or more will be the best for a specific city. We have used all three and found the Bradt guides are best for eastern Europe although the Lonely Planet guide was best for Ukraine. Remember, by the time you buy a guide it is more than likely at least two years out of date and maybe will be four years out of date. We do a lot of our own research and start by doing a computer search for a specific city and tourism there. Or, hotels, Budapest or something like that.

I have used Wikipedia to research the history, etc and from that you can usually find a link to each locations tourism bureau, gives you info on everything. Then when you decide which museum, cathedral, etc. that you want to visit, look up info on trip advisor, works well for us.

Thank you so much for your great suggestions! I will try them.