Another option in that space would be the Fujifilm X-series, as they use the same Sony sensors as Nikon/Sony. They lack tethering support, so you're limited to an intervalometer/remote, but it depends on your needs.
The X-A1, X-E1, X-M1 all lack an anti-alias filter, so you get sharper results. The bundled Fujinon lenses were generally of better quality than your average kit lens too.
Having said all that, I'm a big fan of the ol' Canon 1100D...nice deep wells, low noise, bargain basement
There's a risk you might be underwhelmed going from a 350D to a 60D, as I've always found the 18MP sensors to be noisy compared to the 12MP sensor in the 1100D (but just my opinion).