The gravel road from the state hwy leading to Ballarat is in good shape, as well as north from Ballarat to Surprise Canyon. The trailhead is known as the Chris Wicht Camp, although the camp itself burned a couple of years ago. It's an easy drive with a rental. As far as going south of Ballarat - it's fine for the first few miles, at least to the Brigg mine, which was reopened a couple of years ago. Much beyond that and you'll need a 4x4 - it leads to Goler Wash (where they just discovered the remains of some missing German tourists from 1996) and also the cabin where Charlie Manson and his followers were holed up.
A good source book is Andy Zdon's "Desert Summits".
Also - have you considered getting some traction for your feet? Something like Kahtoola's Microspikes work great on everything from sneakers to plastic mountaineering boots. The spikes are small (hence their name) and don't weigh too much. That way if you work your way up high and find some snow/ice in a shaded area you'll be less likely to fall on your kiester.