A good friend of mine has a KTM excf500. It is very capable off road. He has bags that he can strap onto it for multiday trips. It's just a matter of getting the correct tires for street use. He runs DOT knobbies, which limits the stability at high speeds (above 60mph or so).
I went from a DRZ 400 to a KTM excf350. It's street legal, but it is very light and nimble. The 50/50 ties that came on out were fine for dual sport riding or roads, but I am running DOT knobbies for riding in mud & hill climbs.
When your done with the DRZ, you may want to check out the KTMs. There are a lot of good bikes out there.