Hi Mark -- we took this tour last summer and enjoyed it a lot! Definitely plan on several days in Prague prior to the start of the tour. There is so much to see and do there, and your days on tour won't be enough. We stayed in the Lesser Quarter prior to the start of the tour, and it gave us a whole different feel than that of Old Town. I'd recommend that.
If you have a lot of time prior to the tour, you might want to consider what we did -- flew into Vienna and spent 5 days there, then took a shuttle to Cesky Krumlov and spent 24 hours there, then took a bus to Prague. Vienna is a very easy city to navigate on your own, and our travel route minimized time in transit.
After the tour I would suggest you either plan on a couple of days in Ljubljana (it's a lovely small city and your time there on the tour will be quite limited) or do what we did and take a shared car service to Venice. Venice is only about 4 hours away if you go by car.
Free time on the tour: the interior of the Parliament Building in Budapest is amazing, but you can only see it on a guided tour. English tours sell out way in advance, so if you are interested in visiting on your free afternoon, book before you leave home. Or if you want to be more flexible, you can simply show up at Parliament and sign up for a tour in another language....since the main point of the tour is just seeing the amazing interior. We signed up for a French language tour. There was an English language tour offered at the same time. IN HINDSIGHT once we got through security and went to collect our headsets, we should have requested the English language headsets and just joined in on the English tour, since they were basically overlapping. I had not realized this was the case (and as someone who is reluctant to break the rules, didn't want to tag along on a tour that was sold out....but as both tours were pretty much in the same places most of the time, I could have easily done so.) We took a mid afternoon tour and then went to the Baths quite late in the afternoon. That ended up working out well, because our tour mates who went to the Baths earlier in the afternoon had to wait in line because they were at maximum capacity. By the time we arrived the crowd had thinned out quite a bit.
In Krakow, the Schindler Factory is well worth seeing. Very well done and very moving.