I spent 9 days in Prague and I have the opportunity to see many sites. To me the most impressive ones are: the Loreta, the Cathedral of Saint Nicholas, the Spanish Synagogue, the Cathedral of Saint Pater and Saint Paul at Vyserhad, the Municipal House, and the St. Vitus Cathedral.
This was my second trip to Prague. In my first visit, I took a tour, which was a mistake. Majority of tours take you only to the main entrance and you will have a very limited visit to the cathedral that only allows you to see some windows and the roof. I strongly recommend to pay the ticket to visit the cathedral. The ticket is not expensive and allows you to see 4 sites including the Royal Palace, the Saint George Basilica, the Golden Line, and the St, Vitus Cathedral. You may spend a whole afternoon visiting these sites and all of them are impressive. The ticket costs approximately 10 dollars. I arrived at noon on a beautiful Monday; there were no lines. The Cathedral is not crowded as most tours do not go inside and stop at the main entrance; in addition, not many people pay for the ticket. The visit is actually relaxing and quiet; you will find mainly independent tourists.
Saint Vitus Cathedral has very impressive windows and roses. The two roses describe the life of Christ; there is an art nouveau colorful window depicting the saints of the Czech republic; this window was painted by Mucha. The music hall has beautiful décor, the side doors are beautiful, the golden portal is magnificent, the tomb of Saint Wenceslaus is really nice (the paintings, the door knobs, etc.), the tomb of Saint John Nepomuceno is an impressive baroque tomb made of silver, the roof is lovely, etc.
You have to read online on the sites inside the cathedral or have a good guide book. It is easy to understand. The cathedral was built over a period of almost 600 years and because of this, it is eclectic as it depicts many art styles in a single building (gothic, baroque, neoclassical, art nouveau). The Cathedral dominates Prague and you can see it from almost every place.
Once outside, walk around the cathedral and look for the rooster, the golden helmet, and Sigismund, the big bell located in the roof.