What an awesome trip! I'm JEALOUS.
In Barcelona, Barcelonetta is nice if the weather is good. It's a neighborhood by the water - somewhat touristy, but still lots of nice cafés and bars. There are a bunch of side-streets off Plaça Catalunya that have both touristy stuff and almost secret little squares to wander into. And actually, as not "off the beaten path" as it is ("isn't?"), the Gaudi stuff - Park Guell and the cathedral are definitely worth seeing. A little farther afield is Heliogabal - my favorite little bar (in Barcelona, that is):
http://www.heliogabal.com/home.phpThey have music (I've done a solo show there), but it's a tiny place in a cute and quiet little neighborhood (called Grácia - which is actually becoming kind of "hip," for lack of a better term, so you might find more cool stuff there, too), so they keep it mellow - very friendly!
In Rome, there's a weekend outdoor market in Trastevere that has some of the most amazing bootleg clothes - it's worth going to just to gawk at the Italian version of "Engrish" - "Lonsriver" (as opposed to "dale"), "Scottish Lion" (with the Pringle logo), "Frendi," etc. I guess you could call it... "Ingrese?" I found a crazy jacket there that had black pleather sleeves with "U.S. Motorcycle Club" patches, a green felt (like a high-school letter jacket) front, with some other non-existent American organization's monogram, and an orange felt back with a huge embroidered reproduction of a Blake Babies flyer from the Middle East in Boston! So random - so bizarre!! And that kind of stuff was EVERYWHERE. Worth a stroll through (but I second the "watch your pockets" sentiment)...
Oh - and just for the record, I DID buy the jacket, but it was a gift for someone who used to work at the Middle East.
Have fun!