Luebeck or Lueneburg?

I've only been to Luebeck, but I thought it was wonderful. Happy planning!

I enjoyed Lubeck because of its unique architecture as the capital city of the Hanseatic League. Lubeck’s historic core is also much larger than Luneburg, so you can explore it during an all-day daytrip.

Lübeck is wonderful. I absolutely loved my day trip there from Hamburg.

It might be worth scanning the special events planned during those September dates. The city's tourism site might be useful. A check using one of the AI/LLM software sites might also be useful. It appears there's an Octoberfest in L'berg (Sep 11-14) & a jazz festival in Lubeck (Sep 3-6), among other activities. I haven't confirmed these. I'll leave to you to check if interested.

Ideally go to both. On my fuirst trip to Germany in 1971 , I made it a point to go to both Lübeck and Lüneburg, the first two places I visited in Germany.

Which guidebook?

Both are historic going back to the Middle Ages or earlier. Lübeck was one of the first cities along with Kiel, Rostock to be plastered by bombs when the British began raiding by air in early 1942 and targeting the Zentrum of the towns.

On the other hand Lüneburg escaped the ravages of war intact, undamged, was quickly occupied by the British after they crossed the Lower Elbe. My choice: see Lüneburg, its churches, especially the Johanneskirche , a few minutes from the train station and the Zentrum starting at the foot of the "Am Sande"

If you want to devote more time in this general area by seeing another small historical town, see Lauenburg an der Elbe.

Both are worth a visit.

Lübeck is the more comprehensive package incl. Travemünde - it is just more to see.

The historic background is a little bit differing. While Lübeck has its time as somehow capital of the Hanseatic League for centuries, Lüneburg became rich by salt trade. It was also a member of the Hanseatic League but less important compared to Lübeck, Hamburg or Bremen. Little disadvantage of Lübeck imo is that it is not a small town although the old center is still walk-able. Unique food for Lübeck is Niederegger marzipan.

Without the wish to make your travel more complex: Schwerin is a great destination with some very nice old town parts, main differentiator is the World Heritage castle ensemble. Historically the main difference is that it was the capital of the (Grand) Duchy Mecklenburg-Schwerin which was interdependent for centuries.

The smaller towns Wismar (at the coast) and Ludwigslust (train stop-over between Hamburg and Berlin) are also worth visiting. Ludwigslust has a beautiful palace.

Have a good journey.

I would pick Lübeck if I could only pick one. However, my first choice would actually be Bremen, but that's because I absolutely love it there.

My other choice off the beaten track is Glückstadt, a smaller town but absolutely adorable. The harbor is very similar to Copenhagen's Nyhavn, but without the crowds.