(I'm unsure of the legality of roller-skating as transport in these cities.) It's not necessarily frowned upon, just extremely unusual (roller-skating as a means of transport is uncommon in the USA). Note that sidewalks in all of these cities may be quite irregular, i.e. bumpy -- the norm is concrete slabs, which may have fissures between them. Also common are asphalt sidewalks, which are intended to be smoother, but inevitably get broken up and occasionally potholed by tree roots and weathering.
I don't roller-skate, but I imagine that those properties of sidewalks would probably be significant obstacles to roller-skating. That's not to mention that the sidewalks in some of these cities (e.g. downtown Manhattan) can get extremely crowded, to the point that roller-skating freely is practically impossible.
Note, however, that there do exist paths that you could use for roller-skating: usually these are recreational trails for general jogging/cycling/etc. However, as a means of transport, I think you won't find your roller-skates very useful in the USA.
Finally, to answer your question of is it safe: well, it probably won't kill you to go roller-skating in these cities. It'll probably just be quite inconvenient.