You have to cross the Hudson River somewhere, so its bridges are natural choke points. The three closest to, but not entering, New York City are:
New Tappan Zee Bridge on I-87/I-287/NYS Thruway, toll $5.00 eastbound
Bear Mountain Bridge on US-6/US-202, toll $1.50 eastbound
Newburgh-Beacon Bridge on I-84, toll $1.50 eastbound.
The bridges further north ...
As correctly stated by @MichaelSeifert, it is a graphic representation of a coin.
A circle alone wouldn't be easily interpreted as currency. I speculate that using the dollar symbol would be biasing in an international context, so using a digit is the most intuitive way to display that the circle has value.
Historically, on US tollways you often used a ...
No, you do not need a vignette but might need a environmental sticker in some cities:
Numerous cities have set up or decreed environment zones to reduce pollution in their city centres. Vehicles with particularly bad exhaust values such as old diesel vehicles without particle filter systems and vehicles with petrol engine and an insufficient exhaust ...
It's simpler than you might think.
Look at the map (with tolls removed), decide which roads you do not want to travel on and use an alternative route.
A quick check of the geography shows that alternative bridges are a ways upriver, the I84 doesn't add that much time.
You don't need a vignette in Germany. But for most of the cities you will need an environmental sticker.
This sticker is also needed for foreigners! You can order one before going on your trip and don't get fined entering the first German city on your trip.
official environmental sticker source
Nate has rightly pointed out the three bridge options for minimizing the toll expenses while traveling through NYC. Among them, the most economical would be Tappan Zee Bridge.
Say you travel between Silver Spring, MD and Amherst, MA regularly. The usual route is to take I95 through George Washington Bridge which costs around $40 in tolls whereas if you take ...
I agree with Andrew. I travel between Olney, MD and Hanover, NH. It's simple. I put my address, with destination as Hanover, NH and then I put Tappan Zee Bridge as a "stop" and that's it. It will avoid all the NYC stuff. Much easier drive too.