Following on the excellent suggestions of Chani, Barbara, and Jennifer: the easiest way to accomplish what you are looking for is to pick one country (or two countries in a small region), start with the famous capital and other "brand name" cities and areas, but then go outside them.
Go to Poland and see places outside Warsaw, Krakow, and Gdansk.
Go to the Czech Republic and see places outside of Prague and Cesky Krumlov.
Go to Hungary and see places outside Budapest.
Go to France and see places outside Paris and the Riviera.
Go to the UK and see places outside of London, York, and Edinburgh.
Note that the specific places I mentioned are all worthwhile, but getting out of them will give you the "unfrequented cities" experience you desire. For instance, I believe something like 90% of all tourists to the Czech Republic never see any place in the country but Prague. I really liked Prague, but I also enjoyed Olomouc (covered in Rick's book). In Hungary, I enjoyed Budapest, but also enjoyed Pecs (in Rick's book) and Vac (not in Rick's book - I found it in Frommers).
If you want a more specific itinerary, you'll be very interested in my trip report about Glasgow, Manchester, and Liverpool. The first two get few tourists, and most tourists to Liverpool seemed to be from other parts of the UK, but I had a great time in all three: https://community.ricksteves.com/travel-forum/trip-reports/uk-trip-report-glasgow-manchester-liverpool-in-september-2016
If you tell us where you're flying from, we can give tips on flight options. But Nigel has already given the most important one: always look for "multi city" or "multiple destinations" when flying open jaw, rather than two one way tickets. There are exceptions, but many airlines charge much more for two one-ways.