So, Krkonoše (Giant Mountains) is highly visited area not just because our highest mountain (Sněžka at 1602 metres) is there. It is popular destination for winter sports as well as for all kinds of summer sports including hiking. Just with hiking, you could spend weeks there... especially when mushrooms and blueberries start to grow. But be aware of the fact you are in national parc and it is not allowed to go outside of official trails.
More about Krkonoše generally including many photos: http://en.wikipedia.org/wiki/Krkono%C5%A1e
I was there couple of times, climbed Sněžka in April when there was still snow and we sledged down on a slope... but the best visit was a 3 days hike which I am going to present you here as a suggestion for a long weekend. It all started with geocaching and perfectly planned multi-cache called "Krkonose Crossing" - http://coord.info/GC1KVVN - in English, too. It takes you to the main red trail across the ridge and most people finish in less than 2 days. However when you are already that far why not make it 3 or more days?
Start in Harrachov - it takes less than 3 hours to get there by bus (direct) from Prague. Or take a train to Tanvald and then change to local train to Harrachov - it's a unique and beautiful railway! (specific details at http://en.wikipedia.org/wiki/Cog_railway_Tanvald%E2%80%93Harrachov)
There is quite a lot to do in Harrachov itself but if you want to finish at Luční bouda this day you should hurry up:) Head to Mumlavský vodopád (waterfall) following blue sign. Continue further to crossroads at "Krakonošova snídaně" ("Krakonoš's breakfast") where you turn left (and up!) towards Vosecká bouda. Yet further up and there you are, at the red trail following Czech - Polish borders, called Polish–Czech Friendship Trail (Cesta česko-polského přátelství) which you are going to follow for a long time now... more details about the trail at http://en.wikipedia.org/wiki/Polish%E2%80%93Czech_Friendship_Trail
Take a breath, enjoy the views... and continue towards Sněžné jámy. And Petrova bouda. And Špindlerovka. And Slonecznik. Hate me already? :) Last part! Enjoy the fantastic view to the lakes (Wielki and Maly Staw) and soon you'll reach crossroad where you turn right, taking yellow to Luční bouda to sleep over. It is not exactly cheap but you don't have to go anywhere down and you stay on the ridge. Plus now they have their own brewery, beer spa, sauna, restaurant etc. Cheapest accommodation is 300 CZK with your own sleeping bag or 400 CZK without it (or more as the luxury goes up:) http://www.lucnibouda.cz/en/
Map: http://mapy.cz/s/7Cx3 (red trail; Luční bouda in right below corner)
Get up, have a breakfast, have a look around outside... See it? Yes, Sněžka. Take blue trail across moorland to Obří sedlo. Then it's clear - red trail and up! It's worth it... 
You go down on the other side and continue on red towards Jelenka, Nad pomezními boudami etc. There are quite many places to eat at "Malá Úpa - Pomezní boudy" - try for example the divine blueberry dumplings!
Take a green trail now. You'll still follow Czech - Polish borders go through "Pomezní hřeben" (Border ridge). I can't tell you exactly where you'll finish not to spoil the geocache but I promise beautiful views and rewarding hike.
We then went down and slept at this pension - and I really liked it (and the owners and their hospitality, too!) - but their prices went up a lot since then though... now 650 CZK per person / day incl. breakfast, I hope it's still worth it http://penzion-jonas.webnode.cz/cenik/
Third day, we first took green trail going south (up to "Pod Starou horou" crossroad where we changed to blue to a spa town Janské Lázně. Nothing extremely special but a very nice mostly forest hike (and kilos of mushrooms at that time). Map: http://mapy.cz/s/7CxL
There are some direct buses to Prague (almost 3 hours) or you may change in Jičín depending on the connection.
