Hey,
I've applied for a visa multiple times & you don't need an appointment. You just show up. You do have to show your bank statements to show you have enough money for traveling & if you're on a work visa then they'll particularly look at your salary income - not the amount but just that you've got a salary coming in every month.
The hotel you mentioned is in Greenpoint which is a pretty good central area & Safe. You can book yourself & definitely don't have to go through an agency. I always book my hotels online on booking or agoda. But i would just suggest look up the areas you're booking hotels in as there are some areas you don't want to be coming or going out at odd hours to. Just be careful as you would in any other country with your belongings & not flashing expensive jewellery or cameras & also have your bag on you.
As for wine tasting just book a wine tour with one of the travel agencies if you're interested in seeing a few. We did that the first time we went as its a easy way visiting a few vineyards in one day.
If you're not renting a car then definitely use Uber. They're cheaper & much safer.
Hope this is helpful :)
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