Well you've got the timing going for you, June in Vermont is about as close to paradise as you can get. The weather is usually absolutely beautiful, the trails are generally dry enough to hike, the lake is starting to warm up a bit, life is good.

If you're flying in to VT you'll be landing in Burlington. If you enjoy being on the water there are some fun things to do on the lake. Burlington Surf and Sail Club does windsurfing lessons which are a blast, there's a place that rents paddle boards and kayaks by Oakledge Park, or if you have a little more experience on the water (and money) you might enjoy seeing if you can charter a sailboat for a day.

For hiking, it's all there. Hard to go wrong. You can't really go wrong hiking Mansfield, but if you're up for a drive you might enjoy heading out to Lake Willoughby.

If you like biking there are loads of trails throughout the state. There are rail trails for longer trips, mountain biking trails all over the place, and if you're going to spend more time around Burlington there's a trail that runs along the coast and out to the islands in the Lake. You can grab some creemees out there for an authentic VT summer day experience.

Depending on when you get here you might be able to hang out at Jazz Fest in Burlington, lots of times they'll run public concerts down by the lakefront. You can either go to the concert or listen to it from Foam Brewery across the street. I go every year, it's a good time.

Regardless of what you do, VT is always worth visiting in June IMO. Even if you just sit outside by the lake and enjoy the breeze for four days it'll be worth it. People don't get to experience great weather here too often and the vibe when the sun finally comes out just can't be beat.