I'm planning a trip to Trier and the towns of Fohren and Neurath ( great grandparents emigrated from there). How many days should I plan for to see everything and take in the countryside?
I suspect you are referring to Föhren (Foehren is the alternative spelling) and Naurath.
Not sure what you want to see/do exactly - and that of course will determine the length of your stay.
The Mosel River between Bernkastel and Cochem is pretty spectacular... old world villages, wineries, river cruises. It can be a nice place for biking if that's how you hope to see the countryside. Saarburg is quite nice... The Völklinger Iron Works, like parts of Trier, is a UNESCO World Heritage site. There is a German WW II Bunker in Irrel and another in Besseringen. Luxembourg - the city and the country - might interest you - and George Patton, along with many other Americans, lies in the American Cemetery just outside Luxembourg. So this could be stay of a couple days or a couple weeks.
Russ had a great response.
I suggest about 4 days to include Trier, Luxembourg city and Vianden as well as you family connection places.
to see everything and take in the countryside?
What is everything? Which countryside?
The one city and two towns? The Mosel valley? Wineries? The entire Rhineland, which would include the classic Rhine River Valley between Mainz and Koblenz? Festivals? Castles? History? WWII, Roman or something in between … like the Holy Roman Empire…which might take you elsewhere.
We spent a week from Trier to Koblenz and Boppard on the Rhine. Didn’t see everything.
Do you still have family in the area?
I should give you a more considered and considerate reply. My earlier reply was meant to suggest that you consider what there is to see. But it was less than helpful.
Only been to the area once, this past September, so I am no expert. But I can say that.Trier has a great museum that includes a lot of the history of Rome in this area, close to 2000 years ago, as well as some Roman ruins. Definitely worth spending some time, there, particularly the museum. Also there isthe church that Emperor Constantine established in Trier in the 4th C., as well as a Gothic Cathedral and a market square.
We cycled the Mosel Valley and there are many nice towns, vineyards, lovely countryside, and castles at Cochem and Burg Eltz, a relatively short bus ride from the river.
We did not spend enough time in Koblenz to see its museums or cathedral. But it has a lovely medieval city core that was far more intact than I expected after WWII.
See Rick Steve’s stuff on the Mosel River at https://www.ricksteves.com/europe/germany/mosel-valley