There's a Flickr group here where someone was asking about good skyline views. Someone replied and suggested the Willowbrook Drive view, and posted two of their photos of it.
https://www.flickr.com/groups/948762...7606631658281/
One of those also suggested Rigsby Drive and a few other streets around there that have views of downtown.
Streetview:
https://www.google.com/maps/@29.3973...7i13312!8i6656
Basically, you can jump on Google Earth and look for any street that terminates at downtown or that at least makes a beeline toward downtown and expect there will be a view.
Fredericksburg, Babcock, Bandera, Houston, East Commerce, West Commerce, Roosevelt, South Presa, South Flores, Nogalito, Frio City, West Martin, Buena Vista, San Pedro, McCullough, Broadway, Guadalupe. All of those streets have skyline views at some point. You can scope them out with Google Streetview and even add placemarkers so that you can visit them.