This would be my suggestion for a nice day trip:
with a whole day, I would suggest taking the train to Rostock (main station), change for train to Wismar. Leaving at 8am, you should be in Wismar for 10 am. (train takes just over an hour, no change) The train station is within easy walking distance to the city centre, which is very walkable. Maybe stop for a coffee and some nice cake at one of the many outside cafes on the market square. Either walk through the city centre or take one the tours offered by the tourist information. Maybe spend a couple of hours just exploring. Take a train from Wismar to Schwerin (direct, app. 30 minutes) and arrive in Schwerin for a late lunch. Visit the castle and explore the city. leave around 5.30 so you are back in Warnemuende for 7pm (one change in Rostock). You won't have time to explore Rostock but I recommend you go for dinner and a stroll in Warnemuende which is very pretty, lots of small old houses, geat restaurants and a nice atmosphere just strolling along the beach / harbour area. It is a tightly packed day but would give you 2-3 hours in Wismar, 4-5 hours in Schwerin and then a couple of hours in Warnemuende, so you have time to stroll and just take in the main sights in each of these towns / cities. I hope you enjoy your day!
If you heart is set on Luebeck, take the train from Rostock to Lübeck which takes 1:47 minutes with one change in Bad Kleinen. Trains from Luebeck to Schwerin take just about an hour, again with one change. So it can be done but will spend a bit more time on the train / changing, losing about 1.5 hours of your day with extra travelling.
This is a great cruise port with a lot to see and do. The only problem with this region of Germany is that it is not as language friendly as places like Frankfurt, Munich or Hamburg. As part of the former East Germany, most people over 20 do not speak English at all and most younger people have only basic, school English. Getting to Schwerin and Lübeck on the same day is theoretically possible, but will not give you enough time to enjoy either place. You need to make a choice.
If you just want to see the places, you can go on your own. If you want to learn anything about these areas, take a tour.
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