What is your definition of a day trip?
What mode of transportation?
How long are you there?
Can you speak Czech?
If not can you speak German or Russian?
There are a lot of good places to visit in Boehmen, I have been pretty much everywhere in South Bohemia, I have yet to go to Prague, just because it is another big town that has little to offer except for shopping malls, McDonalds and tourists.
But there is a lot of stuff to see around Czech, but it helps if you can speak Czech, or German, or Russian. I can speak both German and some Czech so there are less limitations.
One day trip however that is both nice and I think you can do without a language other than English would be Karlovy Vary (Karlsbad in its original German). It is a very wealthy spa town in the formerly German speaking part of Bohemia. There are a lot of nice old buildings to see, spas and luxury stores due to the wealthy Russian tourists that like to come there.
You could go to the brewery in Plzen, Pilsner Urquell (the first pils/pilsner beer) is brewed there, I have also yet to make it there, but one day I guess I will go there and to Prag. When I was in Ceske Budejovice (Budweis) there were advertisements for the brewery in Plzen, but not for the Budwar brewery in their own town, it was funny.
Id also recommend making a trip down the highway into Germany and Nuernberg, its worth the trip, its a larger town, but doesnt have the whole "touristy" feel. The town walls are all still intact, the moat is still there, the castle is impressive, the Albrecht Duerer museum (German renaissance painter) is excellent and as I always say, Nuernberg is the best town in Germany.
You would have to pay the highway toll to drive from Prag to Plzen and to Nuernberg, but it would be worth it to go to Nuernberg. I think that I went last two years ago now, my wife had never been there and so on our vacation to the Bohemian Forest, we stopped by Nuernberg.
I am most familiar with Germany as I live here, but I go on vacation every year to Czech and often Switzerland, France, Serbia and Austria, so I can usually help with those countries too.