Hi Dov,
Glad I can finally give you some travel advice!
Was in Prague in early Dec. and will be returning in two weeks. Here's my few cents...
1. Public transport is definitely the way to go. The system is very easy to navigate and the stops are very well-marked. Even from the airport, it was easy to take the bus to the metro. You can buy a two-hour ticket for 26kc, one day tickets for 100kc, or a 5-day ticket for 500kc. Since there was no discount on the 5-day ticket and sometimes knew I would be taking a couple short trips within a 24-hour perid, I just purchased 26kc or 100kc tickets. Do validate them - I ran into officers checking for validated tickets at least 3 times during my stay - once on the way into the city from the airport right after I arrived.
2. Definitely second the recommendation for sturdy walking shoes. You will do lots of walking and the cobblestones are rough on your feet.
3. Most of what you'll probably want to see is in the old town. As a friend said to me - just follow the crowd. I agree with the safety - I was there myself and did not hesitate to take trains / busses / trams late at night.
4. There are two companies that offer two "free" tours (price is based on what you want to tip at the end) - one of the Old Town and one of the castle district. I found the guides to be entertaining and informative. They meet at 10:00 am and 2:30 pm by the Jan Huss statue in the main town square.
5. My favorite meal was a brat from the stands in Wenceslas Square - delish! (and a cheap date)

Bohemia Bagel was good too.
6. Do not miss going into the cathedral at the castle - it's free and the stained glass windows are the most beautiful I've ever seen.
7. If you are looking for a basic hotel, check
www.skoosh.com and query for Hotel Gloria. It was VERY CHEAP, clean, and located a very short bus ride from Old Town. Free wi-fi in the lobby and internet via cable in every room (bring a Cat5 cable).
Have a wonderful trip!
Flygirl555