There's a ferry south near Ticonderoga, which is a pretty cool revolutionary/french & indian war fort that runs daily tours, they even shoot a canon (many an elementary school field trip spent there). There's a bridge not far north of there near Lake George that was recently redone, dumps you into the rolling fields south of Vergennes... about an hour south of Burlington. A bunch of Apple orchards, strawberry/raspberry picking places and a few smaller farm stores that sell maple syrup and such. Vermont Flannel Co. also has a shop on the way to Burlington from Vergennes for all your lumberjack needs.
Hotel Vermont in Burlington is nice, the rooms are very uh.. euro-modern and kinda small but the food there is some of the best in town; you can also get one of the highest ranked IPA's in the country there at the bar (https://www.beeradvocate.com/beer/profile/27039/16814/). Shelburne Farm is worth driving through (or even staying at if you can get a room, though they aren't cheap), it's a preserved estate from the late 1800's that was built by the Vanderbilts. Beautiful property with a good number of hiking trails and so on, right on the lake. The Inland Sea (45 minutes or so north of Burlington) will be the warmest part of Lake Champlain if you want to swim at all.
You'll find the best roads on the eastern part of the state if you're up north. If you head to central/southern Vermont, there's good roads all over the damn place since it's all mountains. The road up to Smuggler's Notch/Stowe is pretty cool, I think it's 108; not far out of Burlington heading East.
A number of ski areas keep their fire access roads open during the summer and I know that a few of them are paved a good portion of the way to the top of the hill. Good views from the top. I wouldn't recommend going up Killington's, it gets really steep in some sections and is all course gravel. There's a gondola you can take to the top for the view though, it runs daily.