Splitting our time between Prague and...?

Olomouc is an absolutely winner, a mini-Prague without the crowds (we were there in May 2011 when it was totally empty--might be different in late June). Also the town of Telc, amazing beautiful small town. We also visited CK, I think you might be right it would be a zoo in late June.

You could catch a train for a 2 hr. ride to Dresden from Prague. It was Europe's most beautiful city prior to the end of WWII when allied bombers did substantial damage. It is finally being reconstructed and has incredible museums and architecture.I
I had relatives that lived there.

Check Rick Steves book: Prague & the Czech Republic. Enough to choose. But of course - what is in R.S. book attracts Ricknicks - and there are many of them. So few tips which are not in his book: Brno - not really small town but smaller and quieter than Prague. Last weekend in June there is a big folklife festival in small town Straznice. The festival is in huge chateau park and also in skansen. Straznice is in very traditional Slovacko region in southeastern Moravia. Wine, women, songs. Many many songs - sound quite different than those from Bohemia (western part of Czech Republic). In nearby Petrov you can visit very picturesque wine cellars called Plze. For pictures google wine cellars Plze in Petrov. You can take a cruise on Bata canal in Straznice.
Or if you go to Olomouc there is an easy bus connection to little mountain resort Karlova Studanka - right under the tallest mountain of Moravia - Praded. 1492 meters above sea level. Plenty of nice hikes there. There are spas there and springs of tasty mineral water. Nice wooden architecture. Google to see pictures.
For beer: Plzen (Pilsen) and Ceske Budejovice (Budweis). You can visit Pilsner Urquell Brewery in Plzen or original Budweiser Brewery in Ceske Budejovice (German name Budweis). They both give tours also in English. Very good beer Bernard is brewed in small town Humpolec in Bohemian-Moravian highlands - picturesque countryside. About 10 km from Humpolec there is hill town Lipnice with the castle on the top. Jaroslav Hasek wrote his famous novel Good Soldier Schweik in the local pub. You can visit little museum of Jaroslav Hasek and also his grave.

with 8 days I would just stay in Prague and do a few day trips.If beer and wine is your thing you could visit a couple of breweries, Plzen is about 90 minutes away by train ,visit the brewery,brewing museum the Patton Museum ,the Synagogue and under ground your, plenty for more than a day.
Budvar brewery is a couple of hours by train
both these place very easy to do on your own.
You could also do a wine tour, never been on one but this link gives a few ideas.
http://www.czechwinetour.com/
Day trip to Dresden is easy enough as are trips within the Czech Republic to Tabor and Kutna Hora both very interesting little towns. Tabor in particular is pretty quiet compared to other places but very interesting.
Within Prague you have a couple of vineyards to visit and try the wine made there ,in June the vineyards will be in full flourish .
warmer weather for me means the Beer gardens of the city and Letna park beer garden is my favourite with stunning views across the city, not as great a selection of beer as Riegrovy sady beer garden (my other favourite) but the view make up for it.You also have numerous micro-breweries in Prague and nearby ,one of my favourite is Berounsky Medved in Beroun about 40 minutes by train from Prague,interesting little town too.
So plenty of stuff to keep you busy for 8 days without having to spend overnights in other places.If you want any more info on anything just ask.

Although not many places in Czechia can beat Telc, it's awkward to reach from Prague: over 4 hours by train.
Olomouc is indeed a beauty, with nearby amazingly attractive Kromeriz easy to reach. Another surprising city is Hradec Kralove, with an interesting mixture of old and early-20th-century new.