Paris to Prague

The train from Paris to Prague takes about 12 hours with 2 connections. It is likely to be more expensive than flying.
The only significant benefit of the train is the much lower carbon footprint. This concern is quite high on my agenda but even then, when the train takes longer than 8-10 hours without an overnight option, I'd rather fly.

As for 3 nights in Paris: that's always better than no Paris at all, and 2 days is just enough to briefly cover Paris highlights

There are no direct overnight trains from Paris to Prague, but there are a few options. Either TGV from Paris to Zürich, and then the night train from Zürich to Prague. Or the night train from Paris to Linz and a day train to Prague from there.

I'm not sure why you wouldn't fly. There are so many non-stop options that take less than 2 hours and cost under $100. Or you could do it at the tail end out of Budapest, same deal.....

But to be honest with you if you are on the 8 day RS Tour then:

Day 1 The RS portion begins at 4pm; but if you arrive a day early there are some fascinating day trips to choose from (i will let the Czech experts here suggest).

Day 2 Prague
Day 3 Prague
Day 4 Prague

and for my taste, that's about enough of Prague

Day 5 is at least 7 hours on a bus to Budapest. My guess is you arrive Budapest maybe around 4pm and then do some drive-bys in Pest with a few short walks in-between and you are checking into your hotel by 6pm? 7pm? Anyone done this tour??

Day 6 sounds like a fairly good overview of Buda and the Pest waterfront area.

Day 7 sounds limited to a trip up Andrassy ut with a few stops.

Day 8 you go home.

No, you need at least on more full day in Budapest and two makes more sense.

So I guess my advise is, instead of Paris, spend a few days at each end of the RS tour.

I'm not sure why you wouldn't fly.

You haven't heard about the problems with using fossil fuels?

Thank you all for your timely responses. We will be adding days to the beginning in Prague and will stay extra time at the end in Budapest.

Hello from Wisconsin,

Good choice on staying extra in Prague and Budapest.

Get the book Prague Walks by Ivana Edwards. Pick a walk or two from that book that won't over lap with the RS tour. I suggest the walk that starts at St. Peter and Paul cemetery. It might be the best cemetery I have ever visited for two reasons. Who is buried there and the sculptures.

Budapest. Take swimming suits along and go to the Szechenyi Baths in City park.

Save Paris for another trip.

wayne iNWI

Thank you Wayne.
Safe travels to you.

My favorite guide books are Eyewitness

https://www.amazon.com/DK-Eyewitness-Budapest-Travel-Guide/dp/0241407966/ref=sr_1_1?crid=2LZUICOF798MT&keywords=DK+Eyewitness+Budapest&qid=1658093545&s=books&sprefix=dk+eyewitness+budapest%2Cstripbooks%2C162&sr=1-1

https://www.amazon.com/DK-Eyewitness-Prague-Travel-Guide/dp/0241533317/ref=sr_1_5?crid=2CBA0UBCWRSVL&keywords=DK+Eyewitness+prague&qid=1658093568&s=books&sprefix=dk+eyewitness+prague%2Cstripbooks%2C109&sr=1-5

Good point.
https://sustainabletravel.org/our-work/carbon-offsets/calculate-footprint/
$2.08

Unfortunately it's not that easy. Paying a bit of money to a website won't make the problem go away. https://www.youtube.com/watch?v=EIezuL_doYw