Depending on "high" in elevation there are free public places that will, if nothing else, get you above street level, with views over streets and long avenues. These include the High Line Park, which is usually open till a couple of hours after sunset depending on the season, or Tudor City, above 42nd Street, which is a street and open 24 hours.
There's also the Manhattan Bridge with some great views of lower Manhattan (I've never walked over the biking path on the other side, but I'd imagine it has fantastic views, too). It has a fence, but you can kind of jam a camera lens through between the top and bottom parts, plus there's numerous rips and tears in the upper chain-link fence.
You can get some decent skyline views from near the middle of the Brooklyn Bridge as well, without it being obstructed by suspension cables. That's also open 24 hours a day.
In Brooklyn there's the Brooklyn Heights Promenade, a public park, which is quite a bit higher than the East River and the streets of Manhattan's Financial District across the way. Depending on the time of year you can see fantastic sunsets behind Manhattan from here.