I recommend going to Luisa Via Romas boutique in Rome, it's called De grillis Boutique and is located in Via Campo Carleo/Piazza grillo behind the Forum of Trajan.. It's kinda hard to locate, really off-track, so I'd do an online search for the adress and print a map if I were you..
Another faboulous store, Nuoyrica (they have Chloe, Balenciaga etc) is located at Piazza Pollarola/Piazza Paradiso near Campo de Fiori.. Would also print of a map of this to get there easy.
Otherwise along Via Corso there are a lot of stores (high street stores like Zara, Sisley etc etc) and eventually along that road you'll get to Via Frattina with some nice stores (at the top of via frattina there's a great store which I can't recall the name of, that carries Marc Jacobs and Rick Owens stuff..)
All the high end boutiques (YSL,
Prada, Hermes, LV etc etc) are at Via Condotti which you'll find along Via Corso, close to Via Frattina.
If you follow Via Baumbuino by the Spanish steps there are also some really nice stores, like Chanel, and store called TAD - a concept store that carries Chloe, Derek Lam as well as furniture and other stuff. Really cool place!
Have a lovely stay in Rome!