Czech republic will open its borders to many European countries after June 15th. But it does not necessarily mean freedom of traveling because some countries may not allow the travellers in.
Czech government issued a map of Europe called the traffic lights that shows where it is safe to travel. You can travel to green and orange (yellow) without the need of the negative covid-19 test on the way back. Red countries are the one with high risk and you would have to prove negative testing on the way back to the country. Foreigners traveling to the Czech republic from both red and orange countries will have to have the negative test.
What the map does not show though, is whether other countries will let you in if you travel from the Czech republic. So far some of them are still quite strict when it comes to tourist activities. Traveling portal cestujlevne.com therefore offered an alternative map that shows where you can travel. But the authors themselves say the safest way to prevent yourself from being refused at the border is to check with embassy of the country you want to travel to.
Just one example for all of how complicated the situation is right now - Germany. It is a green-light country which should mean that traveling is allowed. Yes, traveling is allowed but only for emergency purposes or serious reasons. Border control can decide whether your reason to travel to Germany is good enough. That means still no tourists and no shoppers are allowed.