Most of the tourist attractions are walkable in Rome from many hotels. There are some things which are further out; however, Rome has a good public transportation system. You won't need taxis.
For example, if you want to see the Roman Pyramid and the graves of the English poets Keats & Shelly, you can take the metro to the Piramide stop and you're right across the street from them. You could walk there from Circus Maximus (I've done it), but it's a fairly long hike. I use the Venere.com site for hotels here in Italy.
In rome, the most centrally located places for walking to the attractions are: Colosseo Foro Romano, Pantheon, Trevi, Navona, and Piazza di Spagna. The Repubblica area near Roma Termini train station is a little further out, but tends to be cheaper. http://www.venere.com/italy/rome/ Three places in rome that I've liked are: http://www.
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