I'm going to Prague in Czech Republic, anything else a tourist should do?

Travelling for work give me great opportunities: I can discover new cities, and the next one, as you may know, is Prague. Funny enough, even if Prague is a popular destination, it's the one I have fewer insight on what to do as a tourist. There is a lot of suggestions on the web, but nothing that excited me like in other cities. Don't get me wrong, I'm so happy to visit Prague, but I think I need to find new things to do.

So for now, from what I found on the web, my list will include:

• The Prague Castle;
• St. Nicholas' Church because I like to visit one church in every new city: their architecture are amazing;
• The Lennon Wall because I like the Beatles;
• Old Town (Stare Mesto) will be a nice place to walk, and discover the city, and his treasures;
• Astronomical clock because it seems to be one of the main attraction of Prague with the castle.

On the food side of the experience, I got a lot of good suggestions:

• Brewbar is a coffee stand at the Naplavka farmer's market. The owner is an amazing barista we hired for the Firefox OS booth at the Mobile World Congress. It was the best coffee I ever had, so I'll repeat the experience there;
• Strahov Monastic Brewery for a good local beer;
• Čestr Ambiente for a good meal;
• Lokál Dlouhá seems to be a nice little restaurant for something fast, but fresh, and tasteful;
• Café Imperial for another great meal.

For the prepaid sim card, I think I'll go with Vodafone except if you told me not. I've been served well in many European countries: the network is usually good, and the price is cheap. They even have a stand at the airport, which I like as it will be easier for me.

As usual, I'll find a Starbucks to see if they have local coffee mugs, and I'll do one or more geocaches, but is there anything I'm missing? Anything in my list I should skip? Any attraction I need to see or activities I should do? I know I need to taste one of the Czech Republic speciality alcohol called Slivovitz, but is there any typical food I should try too? Help me make this trip even better than it will be!

P.S.: Since you always discover new things once on site, and that some stuff I listed may not be as good as it seems, I'm planning to share my insight, in a blog post form, about the cities I've visited to help others have an even better experience.