I am thinking of visiting Prague for a week in May. I do not want to rent a car nor do I want to spend hours on public transportation traveling to/from my hotel to places of interest.

I do want to see the historic part of the city and be near whatever "must see" spots are there. (I admit to complete ignorance of the city and have no idea of what those spots are.)

Hopefully, I will be able to get to/from the airport without spending a fortune on transportation.

What area(s) of the city should I look for in making my reservations?

(Yes, I know that all of the above are newbie questions. Yes, I know that I am a veteran FTer who should be travel-savvy. Bear with me please -- when it comes to Prague I know absolutely nothing except that it is one of those cities which everybody says is a "must").