Absolutely. Christmas? Budapest is amazing. Then you can do it a second time in Kyiv or Lviv (Orthodox Christmas is January 7).
Beaches? Hard to beat Croatia or Montenegro or Albania ... yes, Albania.
Mountains? Some of the most beautiful are in Bosnia & Herzegovina, Montenegro and Albania
Historic Cities? Pick your period in history; from ancient Prague to Budapest to Istanbul (i'm stretching a bit to include Istanbul in this list but because of its proximity and easy connections it is easy to pair with Eastern Europe) to Sarajevo one of the most culturally diverse cities I have stumbled in to.
Ancient Greek and Roman sites, think Albania or Turkey
Churches and Cathedrals... well, yes, but you get the added 13th century mosques in parts of Eastern Europe and the fascinating Orthodox churches in others....
Villages and Towns (small cities)? Nessebar, Plovdiv, Sibiu, Sighisoara, Lviv, Chernivtsi, Gyor, Sopron, Gjirokaster, Kruje, Banská Štiavnica, Banská Bystrica
Castles? I was amazed by the beauty of the castles in the Czech Republic and Slovakia and by the sheer numbers in Albania.
You can do it through the back door in Hungary and the Czech Republic or through the Basement Window on the back side of the house in Albania, or Bosnia or North Macedonia...... So, so many choices. And cost? You have a choice in the lesser known countries. You can either have a vacation at Western standards at half the cost or you can use the savings to increase your reach and enjoyment.