We were there a few weeks ago.
Buy a Roma Pass - http://www.romapass.it/?l=en
Free public transportation (bus and metro - bus 64 will put you close to most everything but watch your pockets (express bus 40 takes the same route - fewer stops)) and 2 free admissions for archaeological sites (Colosseum + Palatine hill = 1 admission). Most museums are free.
If you are going to hit the Vatican Museums - buy in advance. You can avoid the line (which will be at least 3 blocks long). I recommend the audio tour add-on if you don't choose guided.
http://biglietteriamusei.vatican.va/musei/tickets/do
The fountain at the base of the Spanish Steps was closed and covered for maintenance... dunno if that is still the case. (if you are in that area and see a tailor which sells Zegna suits (it will be a few doors down from an E-cigarette store) get me an email address for them and I'll give you two Pmags)