Ive actually been to most of Europe including the Glamour cities, Countrside and the Alps.
Its the Glamour cities (except for Paris which I hate) that I prefer maybe on subsequent trips visiting the Alps is possible.
People get so defensive, I actually said to go. But if this is your only trip you need to make choices where to go. TCG if you were only able to go to the UK one time in your life would go to Gateshead or London. Maybe you would answer Gateshead, but most people would answer London. I would tell people who visit NYC one time in their live. Dont go to Monsey go see NYC. There is nothing wrong with that, Its not a knock on Monsey, it just isnt NYC.
OP some ciites of Europe are cheap especially Prague ,Bratislava, Budapest , Madrid and Athens. You can probably get a hotel room there for about $50-$100 without much effort.
Its London, Paris , Rome and Venice that are the expensive ones to stay in.