A few months ago, I asked for suggestions to visit Schleswig-Holstein for a week in June. Unfortunately, that planned holiday didn't happen, but instead we've just spent two weeks in and around S-H in September, making use of the wonderfully helpful advice you on this forum provided.
Our trip covered Hamburg, Luneburg (in Lower Saxony), and several places in S-H itself.
Apart from a long weekend break in Munich a few years ago and something similar in Berlin more recently, this was our first trip to Germany.
We thoroughly enjoyed our time and had a very pleasant holiday.
We are rather lazy, slow moving tourists and others could do what we did faster or add more stops. We chose not to hire a car, but one would be useful if wanting to cover more ground in the same time.
Our travel between cities was via the efficient and regular railway systems. Using Deutsche Bahn website to plan. None of our journeys were very lengthy - I think the longest was only about 80 minutes.
We enjoyed plenty of varied food. Both what I take to be traditional local dishes, fish and pork especially, but also plenty of ethnic restaurants - Italian seems particularly popular everywhere. And we had some excellent fish and chips in Kiel which would have been acceptable even in Whitby and a fine Portugese meal in Hamburg.
One last introductory remark. In many of the tourist attractions we visited the commentary or signage was only in German. That didn't concern us, though I was surprised. Occasionally, such as the Luneburg Rathaus they provided an English pamphlet whilst the guide spoke in German. In other places, such as our boat trip around the Hamburg Alster we enjoyed the opportunity to switch off and enjoy the view ignoring the guide telling us what we might actually be looking at. On the other hand, where English did matter such as buying railway tickets or ordering meals, everybody spoke English well and more than enough for us to manage.