I hope also someone else answer here because i live in Torino (north Italy) and i have been in Rome a long time ago .
Mainly when you go to Rome is to see monuments, museums and squares ( square="piazza") .
If you want go for a walk in the city I suggest you to make your starting point the Colosseo and then go for the places around it, a lot of stuff is nearby.
By the way three places you cant miss are :
Colosseo - no need to presentation
Fori Imperiali - most beautiful roman ruins
Musei Vaticani - the cappella sistina is here !!! (reserve a ticket before you go , or you will have to wait a lot in queue )
To grab an idea of what to see use this website (in english):http://www.turismoroma.it/cosa-fare-categorie/da-visitare?lang=en
PS : the planetarium timetable :
-Tuesday-Friday: performances at 9.30, 11.00, 12.30 (ticket office opens at 9.00);
-Saturday-Sunday: performances at 10.00, 11.00, 12.30 (ticket office opens at 9.00) and 15.00, 16.00 and 17.30 (ticket office opens at 14.45);