Two days in Prague

Rick's suggestions are a good start. Take your pick.

https://www.ricksteves.com/europe/czech-republic/prague

Rather than a checklist of museums, Prague is a fine place to wander around and just take in the fun atmosphere. Plan some worthwhile activities — take a self-guided tram tour, hire a local guide, enjoy a concert, or go for a scenic paddle on the river.

In the Old Town
▲▲▲ Old Town Square Magical main square of Old World Prague, with dozens of colorful facades, the dramatic Jan Hus Memorial, looming Týn Church, and fanciful Astronomical Clock.
▲▲▲ Charles Bridge An atmospheric, statue-lined bridge that connects the Old Town to the Little Quarter and Prague Castle.
▲▲▲ Jewish Quarter The finest collection of Jewish sights in Europe, featuring various synagogues and an evocative cemetery.
▲▲ Museum of Medieval Art The best Gothic art in the country, at the former Convent of St. Agnes.
▲ Havelská Market Colorful open-air market that sells crafts and produce.
▲ Klementinum National Library's lavish Baroque Hall and Observatory Tower (with views), open by 45-minute tour only.

In the New Town
▲▲ Wenceslas Square Lively boulevard at the heart of modern Prague.
▲▲ Mucha Museum Easy-to-appreciate collection of Art Nouveau works by Czech artist Alfons Mucha.
▲▲ Municipal House Pure Art Nouveau architecture, including Prague's largest concert hall and several eateries.
▲▲ Museum of Communism The rise and fall of the regime, from start to Velvet finish.
▲ National Memorial to the Heroes of the Heydrich Terror Tribute to members of the resistance, who assassinated a notorious Nazi architect of the Holocaust.
▲ Petřín Hill Little Quarter hill with public art, a funicular, and a replica of the Eiffel Tower.
Church of St. Nicholas Jesuit centerpiece of Little Quarter Square, with ultimate High Baroque decor and a climbable bell tower.
Wallenstein Palace Garden Largest and beautiful Renaissance palace garden.

In the Castle Quarter
▲▲▲ St. Vitus Cathedral The Czech Republic's most important church, featuring a climbable tower and a striking stained-glass window by Art Nouveau artist Alfons Mucha.
▲▲ Prague Castle Traditional seat of Czech rulers, with St. Vitus Cathedral, Old Royal Palace, Basilica of St. George, shop-lined Golden Lane, and lots of crowds.
▲▲ Lobkowicz Palace The most entertaining palace in town.
▲ Strahov Monastery and Library Baroque center of learning, with ornate reading rooms and old-fashioned science exhibits.
Beyond the Core
▲▲▲ Alfons Mucha's Slav Epic Twenty enormous canvases at Veletržní Palace depicting momentous events of Slavic history.
▲ Vyšehrad Welcoming, untouristy park at the site of a former hilltop palace, rich with Czech history and great city views.

I think the list above gives you good priorities. The Old Town and Jewish Quarter are so close together you can visit them in half a day, or maybe a little more, all on foot. Besides the cathedral, I especially liked the Lobkowicz Palace museum. I didn't go to the Mucha sites, except for one of his works in the cathedral (a window?), didn't interest me very mucha.

I suggest an early morning visit to the Charles Bridge if your hotel is close enough. It was jammed in the afternoon when we were there (in June a few years ago), but we came back the next AM and it was magical.

We took an ebike tour on our first evening to give us an overview and it was great fun! Prahna bike I believe was the company.

http://www.prague.net/itineraries-in-prague
this link will give you lots of info, I have set it on the Itinaries page but it will link to other stuff.
Edgar mentions the Slav Epic and it is stunning ,I have been to see it twice but it is going on tour soon and I very much doubt it will still be there next September.
http://livingprague.com/
this is another good website for great info, they also do small group tours (max6) to some of the less well trod parts of the city

For fun fill days including food. Pivo (beer) including the original Budweiser at affordable prices during walking breaks.

http://www.budvarkadejvice.cz/
Edgar have you been to this place,best Budvar in the city and does superb food , real typical Czech stuff, their Koleno (pork Knee) and their ribs are fantastic,I always have to share a Koleno too much for one person.

Unclegus: Your Budvar suggestion looks good but we pretty much dined in Prague 1 (Old Town) where there was no such thing as a bad beer.

Other food and drink suggestion is the rotisserie grilled round hollow pastry trdelník.

yes you are right no bad beerin the city. 2 new places I went to on my last trip both on the edge of the old town Jewish quarter that were good were.
http://www.kolonialpub.cz/
this place is right opposite the old Jewish cemetery, great food and they do Pilsner urquell and kozel dark there , you can even buy Rezane where the float dark kozel on top of Pilsner urquell, really nice , food in great.
http://www.kozlovna-apropos.cz/
this is a fairly new Kozel pub and bloody good, the beer is great and the food excellent, had a duck Burger that was outstanding in there.
I was in the Budvar brewery in October with a friend , the beer from the lagering tanks there is just amazing , worth a day trip from Prague

BTW Tedilnik has moved on a bit , you can still get the original everywhere but many place now make a cone shaped version and fill it with ice cream, not tried it that way as I am not a fan of ice cream but the original version is always a must have snack when I am in the city