For optimal road use, the sizes you have now are the ideal size. You might be able to bump up to a 110/90-19 in the front but fender clearance will be an issue.
In the rear, you have a narrow swingarm, you could probably stuff a 130/90-18 there.
Keep in mind though that your bike has a high center of gravity which may not play well with a dual sport tire.
The ride IS the adventure. The destination is just to get gas!