I would think either town would work, but with Haines being more of a laid back town, it might be easier to leave it there. Have heard that the Hitch-em-up campground has some dry parking where you can park a rig for a few days for a fee. Or stay at the Ocean Side CG and leave your rig at your site for the time you will be in Juneau. You can then walk to the ferry landing, and rent a car and hotel it in Juneau. Lots to do and see in Juneau for a few days.
In Skagway, I would get a site t Pullen CG and leave the rig there. Walk ons the ferry are easy to get and not at all costly. A large dually pickup would not be my choice for a vehicle to run around in Juneau, so I would rent a car for the time I was there. Juneau tends to only get busy and crowded in the winter when the legislature is in session.