We will be on a cruise docking in Hamburg at 9 am one morning and departing at 2 p.m. the next day. Nothing is scheduled during the morning or afternoon on the first day but we have an interest in an Evening cruise of the Hamburg waterways and its botanical park. There is a 3 and 1/2 hour tour of the city on the second day--essentially a bus into the city so folks can explore on their own it appears. Since Luneberg is only 36 min by train I am thinking it might be nice to try to fit in a visit there--probably on our first day. So my questions are these:
Is Hamburg sufficiently interesting to fill the first day as well as time on the second? (we will probably do everything on our own rather than take even the one guided tour) Is it possible to see the major sights of Luneburg in about 3 hours not counting train time? Are the Luneberg sights worth chasing after or would we be better advised with our somewhat limited time to remain in Hamburg and soak up more of what it has to offer?

If you find Hamburg sufficiently interesting for 1.5 days depends a bit on your interests.

The city has a few good museums, and you may want to check the TI website if there is exhibition you might be interesting in.
https://www.hamburg-travel.com/

Otherwise, it's always cool to take a harbor cruise. The major advantage of the Port of Hamburg is its proximity to the city center - literally on the other side of the river. And being somewhat compact, you can actually see lots of "action" on a short harbor tour compared to much more spread out ports like Rotterdam. Not sure if I wanted a late night cruise, though, as you can obviously see less than with daylight.

Not sure what you mean with "botanical park" - maybe the downtown Planten un Blomen park? Which is nice for a stroll but no breath-taking site.

Aside from the harbor cruise, the other "must see" would be the new Elbphilharmonie. The viewing platform AKA the Plaza is free of charge, except for a nominal booking fee if you want to reserve guaranteed and timed access to the Plaza.
https://www.elbphilharmonie.de/en/

The nearby Speicherstadt - which roughly translates to Warehouse City - is also a nice area to explore. If anyone in your group has an interest in model trains, Miniatur-Wunderland is something to keep in mind for a rainy day.
https://www.miniatur-wunderland.com/

As a day trip, Lüneburg is indeed very easy to reach. And 3 hours are sufficient IMO.
The usual suspect for a day trip from Hamburg would be Lübeck, though.
It's as easy to reach by train. Maybe you want to also google Lübeck (or Lubeck) to see which of the two towns is more your cup of tea.

Happy travels.

Cowboy covers the area well, there is a submarine museum near the mouth of the Elbe but unless you are into the things then no reason to go. Hamburg has a nice centre (watch out for bikes as in all of Germany they are often on pavements). I prefer Lubeck to Luneburg but both are worth 3 hours though check out opening times for town halls or other fine old buildings

Cowboy, thanks for the info on Hamburg. Yes, it is Planten and Blumen park. Your comments about it and about seeing the harbor in daylight make me think that we may skip the evening cruise, take a day cruise instead and go into Luneberg on our second day in town.

Cowby and Billbo, I also think Lubeck sounds like the most interesting side trip from Hamburg but even though the trip by train is longer from Kiel we will be taking it from there and seeing it on the day we are docked there. Kiel sounded to have little/no interest for us and Lubeck sounded like the best alternative when we are there so we'll already have seen it by the time we get to Hamburg. Glad that Luneberg is available to see out of Hamburg and I now think I have a pretty good plan for our time in Hamburg. Thanks to both of you.

Makes perfect sense to visit Lübeck from Kiel.
Your gut feeling about Kiel did not betray you - let's say that Kiel has little or no interest (except for the Travemünde beaches in summer) for anyone ;-)