Karlovy Vary: Day trip? Overnight stay? Skip it?

can I ask what time of year you intend to visit. Karlovy vary is a lovely place during the better weather as it is a great place for wandering, enjoying the waters and visiting places like the Diana tower and the various spa areas. In the winter time you could head there for a day of spa treatments if that is your thing ( could do that in any weather). bus from Prague takes about 2 hours. your second option to me sounds better but it will take 5 or 6 hours to get there by bus or train but an early start should give you an afternoon, evening and a few hours next day to enjoy the place.
From Berlin you could have an overnight in Dresden and a 2 hour or so train trip to Prague the next day, you could still decide on a day trip from Prague to Karlovy Vary if you wish

Although I've been to the Czech Republic several times, I've never been to Karlovy Vary It is a spa town, so you may want to avail yourselves of the amenities. I suggest watching this video about the town. https://youtu.be/USIKzTWZe70 The Honest Guide mostly posts about Prague, but they venture to other locations, too. You could also watch the movie Last Holiday with Queen Latifah, which was filmed in Karlovy Vary. Enjoy, whatever you decide.

We really enjoyed Karlovy Vary when we were there about 10 years ago. And you are right when you say it's a fun change from the rest of your itinerary. We also visited Prague, Cesky Krumlov and Telc on that same trip, and KV is very different from them architecturally, location (surrounded by mountains), and ambience. We enjoyed trying the different waters. You buy a cup and walk around trying the different springs. We scheduled time at a spa which was fun and relaxing. And we also just enjoyed walking around the city and admiring the architecture. KV is a very pretty city. We had good food in KV, too. I remember dining at a restaurant that had tables on a bridge over the river. We were lucky to get a table on the bridge.

I spent three days in Karlovy Vary and I found it to be nothing but a huge tourist trap. I would never go back.

I spent a day in Karlovy Vary a few years ago. As UncleGus said ,it's a two hour bus trip from Prague . My only regret is that I didn't stay there a couple of days. Absolutely a beautiful city with a surfeit of Art Nouveau architecture.

I stayed one, maybe two nights and enjoyed it. I vote overnight stay.

I noticed that lindanny ( posted above ) mentioned " Last Holiday " ( 2006 ) . While filmed in Karlovy Vary , and the cinematography is indeed sumptuous , the film ( it's a remake of the 1950 film with Alec Guiness as George Bird ) is a horrible rewriting of the original JB Priestly script . The message and poignancy of the original is gone ,replaced by a lot of smart aleck humor , and the ending which is a powerful gut punch in the original film is gone , The original film is set in a fictional resort town on the English Channel Coast , and is well worth watching . Sorry to be off track here , but the remake really turned me off when it came out