Prague, Cesky Krumlov, Trebic, Mikulov, Budapest

Suggest you get a guild book or two and figure out what it is you want to see in your destination cities.

They would also have info on transport.

Not knowing how long a trip you plan makes it borderline impossible for anyone to give meaningful advice

Yes, it is very feasible and easy. Train and bus schedule you find here: http://www.idos.cz , You can switch it to English. I would recommend Prague to Cesky Krumlov by train. There is one direct train a day, many others with change in Ceske Budejovice. There are also many buses. Between Cesky Krumlov and Trebic bus would be faster. The same between Trebic and Mikulov. From Mikulov you go by train to nearby Breclav and change there to train to Budapest. There are too many hotels in Prague, Cesky Krumlov and Budapest. Check rick Steves book about Budapest. All your other cities and towns are also in his book Prague & the Czech Republic.

Yes. Go to www.bahn.com and look it up.
Prague to Cesky Krumlov in 3 hours, one 8 am direct train, others with a connection.
Cesky Krumlov to Trebic in 4 1/2 hours with a train change in Ceske Budejovice (grab an original Budweiser)
Trebic to Mikulova (Moravia) in 2 1/2 hours with train changes in Brno and Breclav.
Mikulova (Morravia) to Budepest in 4 1/3 hours with a train change in Breclav.

You can use booking.com to find hotels. Or use google maps and zoom in on the towns to see lodging establishments.

You can use Deutsche Bahn website too but in this case the Czech one (which is in my previous post) will be more helpful because you can also check the bus schedule. When you are searching for your schedule it is important to have correct spelling. It is Mikulov, not Mikulova. Czech Republic consists of two (well actually three) provinces: Cechy (Bohemia), Morava (Moravia), Slezsko (Silesia). So Mikulov is in Moravia.

Did I turn Mikulov into a girl?

Yes. Obviously that's what we prefer.

The logistics of transportation after Cesky Krumlov look challenging. We don't want to waste too much time getting from place to place . Maybe hiring a private guide/driver would be better than using public transportation. Any thoughts/suggestions?

For information on rail travel for your itinerary (and in all of Europe) check out www.seat61.com.

I don't know that getting a private driver will save all that much time. Viamichelin says 3 1/4 hours Cesky Krumlov to Trebic drive time. Train time is 4 1/2 hours with 23 minutes train change time in Ceske Budaejovice.

It really won't save much time. From Cesky Krumlov to Trebic by bus it is 3 hours 31 minutes with one change in Ceske Budejovice.