Prague BJs were so-so. There are about a dozen casinos. I believe some casinos cheat... so becareful. There was one receiving Iserale juket players then dealt (?) seconds on them. I was caught in-between and lost heavily. I read from bj21 that other counters suffered similar insidence.
Budapest: I was there many years ago. I read recently that Las Vegas Casino at Hyatt was OK.
Congratulations on your trip; the wife and I went there a year and a half ago and we loved both cities. Although there is blackjack to be found, I didn't play too much as there was too much to see and do to spend much time in smokey casinos.
The BJ rules in both cities are standard European rules; 6 deck, ENHO, etc., and penetration was 75% at the places I played (but I did not make a complete survey.) All of the casinos I saw were pretty small, and only had between 1 and 3 blackjack tables. As is also the practice in Europe, you have to show your passport to enter.
The general playing levels of the people in the casinos was slightly above what you'd see in the US, but still pretty poor. Nobody on the other side of the table seemed in the least bit bothered by my bet variations. If you know how to track shuffles you will like it as they didn't shuffle very carefully. I did not detect any cheating, but that doesn't mean that it didn't happen.
The other post mentioned the Las Vegas casino at the Hyatt - that one has a nice feature; they play in Hungarian currency in half the casino, and US dollars in the other half. This lets you play without currency exchange worries.
My general advice is to have fun and, as I noted above, there's a lot to these beautiful cities, so don't spend too much of your vacation in the casinos.
If you're going to take the train from Prague to Budapest, you might want to make sure you take the one that goes through Vienna. We were not aware that there are 2 routes; one though Austria (that goes through Vienna) and another that goes through Slovakia, so we took the train that left from the station closest to our hotel. That train turned out to be the one that went through Slovakia. Although Slovakia has its own interests, and we had the first class car completely to ourselves, we were told later that the route through Vienna is prettier.