We have 7 nights. Will fly into Prague and then fly out of Budapest. How many days should I spend in each city? Is 2 nights enough for Prague?
I would give 3 nights to Prague, 4 for Budapest.
I agree with Kenko's recommendations: 3 nights in Prague and 4 nights in Budapest. Why? Two nights is not enough for Prague. Budapest deserves more nights than Prague because it is larger than Prague with more sights. I would not add a daytrip from Budapest. There is too much to see and do in Budapest. We spent 5 nights in Budapest, and when I was planning our trip, I thought we would take a daytrip to Szentendre, but we changed our minds almost as soon as we arrived in beautiful Budapest.
The direct answer is in your other post with the same question (but putting it in both countries is a good idea).
The indirect answer is 7 days is marginal for Prague and Budapest. Sure, 3 nights in Prague in 4 nights in Budapest is the correct stock answer but the cities are so far apart that it isn’t as good an answer as it would be if one were asking about Vienna and Budapest. Travel time eats up a lot. Travel is about the time in the city before bedtime and 3 nights in City X is not the same trip if you arrive in the city at 9am as it is if you arrive at 5pm.
If you take the 7:37 train out of Prague it arrives at 2:28pm. Then there are not less than 30 minutes to get to your accommodation and 60 minutes to check-in, unpack and get back out. Then the first stop is food because you haven’t eaten since 6am. Because you are starving, you go close to the hotel. Yes, you saw some Budapest on the way to eat, but the tour didn’t begin in earnest until after lunch/dinner, so about 5pm. Not much time in the day is left; especially if you have a fussy infant along on the trip. This scenario is not much different than 3 nights in Budapest which is really kind of short for the location.
Okay, so you fly. Ryanair is most often under $100 with luggage. The flight departure varies from about 7:30 to 8:30 so you had to get up at 4:45. But you do arrive before 9:30, drop your bags at the hotel and look around Andrassy ut until lunchtime. Hey, that works, you have a full day in Budapest. But you flew and many hate that.
So, the third option is to just see one city. You are going to be moving slow if you are bringing an infant with you so ….. Or maybe not. But I did with my four.
Prague for 5 nights and Cesky Krumlov for two nights (take the train down and back in the middle of the Prague stay). During the 5 nights in Prague, you do one or two days of day trip. Kunta Hora maybe and there are a handful of beautiful castles not far. I like Karlštejn Castle a lot. You can do them with a private guide, or you can join a tour. Check out Viator.
You mentioned Eger. Okay, another option is 5 nights in Budapest, with a day trip to Tihany and one to Szentendre then two nights in Eger in the middle of the Budapest stay. Tihany is an all-day trip, but Szentendre is a leave at noon, eat lunch in Szentendre, spend the afternoon there and take the 5pm boat back to Budapest.