If you're looking for natural urban space done with a cultural twist, tighten the laces on your walking shoes and head just north of city center to the Villa Borghese. At its heart is an artificial lake, around which an abundance of gardens and cultural institutions have long impressed travelers. Known as a "park of museums", the most famous is the Villa Borghese (after which the park is named), whose reputation is built on an exemplary collection of sculptures and paintings primarily created by Italians.
The Galleria Nazionale d'Arte Moderna is an exhibition of the Italian artistic muse over the last few centuries, while the Museo Nazionale Etrusco has a large selection of pre-Roman artifacts that have been excavated from local archeological sites. Also of note is the Piazza di Siena, an amphitheater around which Rome's largest equestrian event is run every May.
There's no pressure to go culture crazy while in the Villa Borghese, though. If a chance to literally stop and smell the roses is your only agenda, then you'll be quite content as well. Even better, rent a bike from one of a handful of park locations and see the park in a unique way before heading back into the tourist fray.
Note:A great stop on the way to or from Villa Borghese is the Piazza del Popolo, just between the park and the Tiber River. This pedestrian-only square is yet another beautiful example of Roman architecture and sculpture, best represented by the two thousand year old obelisk at its center.