Alright I'm pretty bored at work so here are some of the breweries that I really like
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14th Star - about 20 minutes north of Burlington, but a great brewery. Veteran owned. My personal favorite in the state. There's a burger place attached. Favorite beer from them is
Valor
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Switchback - another favorite of mine, located near the waterfront in Burlington. The classic
Switchback Ale is a must if you have never had it. And get it on tap. Makes a huge difference, no lie. Switchback is available literally everywhere though, so if you only have time to visit a few take that under advisement
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Zero Gravity - great variety of beer, a really nice interior too. Downtown area Shuffleboard and lots of games and some TV's.
Conehead is a must try but also pretty common
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Stone Corral - had tried their beer pretty often, but have gone to the brewery a few times and it has quickly become a favorite of mine. About 15-20 away from Burlington. Really good food too, I always get the mac and cheese with buffalo chicken
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Lawsons - a bit further away but if you're in the area a really good visit. Amazing new facility. Nicest looking brewery I've ever seen. And some of the best beer in the state. I had a
Knockout Blonde there a few weeks ago that was great
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Burlington Beer Company - last time I came here I was pretty impressed with the variety of beers they had, all that I had were good too. Lots of board games there too to keep you busy. And some food
Now if you want to visit some restaurants...
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Manhattans Pizza - located right downtown, probably the best beer selection in the state in my opinion. Every time I've been there they've had Heady Topper, Focal Banger, and other stuff thats pretty tough to get your hands on. Pizza is good too. My only advice is don't go too late. It gets pretty busy as the night goes on, and turns more from a restaurant/pub to more of just a bar as the night goes on. So if you go for a late dinner you may have trouble getting a seat and there will probably be more college hooligans.
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El Gato - good Mexican place also downtown
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Vermont Pub and Brewery - I do not think this place is all that great but it checks a lot of boxes. The beer is average at best. The food is decent. But the good news is it has a lot of both. Its a very safe choice. Nothing amazing but its easy. Better in the summer because it has a great patio.
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Farmhouse - good American style food, great beer selection. Kind of pricey though
As far as what else to do in the area...
Downtown Church Street has a ton of shops, food, bars. Could make a whole day down there just eating drinking and browsing. Can head down to the waterfront, there's a museum "Echo" down there too. Haven't been in years so can't exactly vouch for it. Skiing of course if you're into that thing. I like the other posters idea of going to a UVM hockey game too.
Honestly when I think about it theres not much to do here besides drink a lot so I hope you are down to do that
I'll keep thinking. Let me know if you have any questions