The Angeles Crest Highway (California highway 2--I think) starts in the 
Western Pasadena area and heads North through the mountains and ends up on 
the high desert--I have not personally ridden it--but has quite a reputation 
as a motorcycle road to behold.

Other good rides in the LA area are the Ortega Highway--starts in San Juan 
Capistrano and winds its way inland and dumps you out in Lake Elsinore.  The 
biggest downside to this road is that it's a fairly major commuting route, 
so avoid rush hour times.  If you do this ride, you MUST stop at the Lookout 
restaurant on top of the mountain before you drop down to Lake Elsinore.  If 
you're in a mood to cover some ground, Inland Riverside and San Diego 
counties have some of the best roads you could hope to find for GTS 
riding--not too tight, decent road conditions, lots of long sweepers, good 
weather, blah blah blah.  I like to ride down to Julian and take your pick 
of all the great roads around--they're all good.

A neat trip that takes a couple of hours is called Glendora Mountain 
Road--Heads North out of Glendora into the mountains and drops you off in 
Azusa.  You have the option of riding over to Mt. Baldy and into Upland, but 
the road is poorly maintained, it's very tight and there's frequent 
landslides that leave the road dusty and quite a bit of gravel--not much fun 
on anything and it's really too tight for the GTS.  The other way takes you 
into Azusa Canyon, which can be pretty loaded up with cagers on the 
weekend--off hours are the best times.