The biggest competitor, by far, is high medieval architecture, roughly 1000-1200, but it's a fascination that was shared by many in the sixteenth century. I've read (I'm a bad academic, forgetting a source) that many characteristics of renaissance architecture are borrowed as much from Romanesque as from Roman, as a locally-flavoured, artistically-political choice to emphasize local Tuscan tradition over International Gothic.
Baroque music and sculpture are also high on my list, but many of my favourite aspects can also be found in sixteenth century antecedents. The basso continuo that distinguishes baroque music makes its appearance in the sixteenth century, and layers of polyphonic arrangement are not as universal as they're often perceived. And, while baroque sculpture has an energy and movement that its forebears do not, the realism and humanity of sixteenth century sculpture bring stone to life almost as vividly.
The sixteenth century is part of the Early Modern period in academic discourse, bridging the gap between medieval and modern, and that's precisely why I love it. It retains enough of earlier time periods to feel exotically interesting, while close enough to our modern sensibilities to be approachable. As a performing artist this is key, since my goal is to bring historical music to modern audiences and approachability helps. There is enough that is familiar in sixteenth century art to make a spice out of that which is foreign.