You can easily hit numbers 1, 3, 4, and 5 in the following order:

1) Take the Alcatraz tour [which I highly recommend]
2) Walk to Fisherman's Wharf / Pier 39 / Hard Rock Cafe
3) Walk to Boudin's flagship location on Jefferson St. near Taylor
4) Walk to the north end of the Powell-Hyde cable car line and take the cable car to Union Square.

If you want to ride the cable car in the opposite direction, you could do the above steps in reverse, though I'm not sure the timing on the early bird Alcatraz tour. It's not a long walk between the above locations.

If you like ice cream, you might also consider adding item 3.5 between 3 and 4 above: Ice cream sundae at Ghirardelli.

It's easy to reach the Ferry Building by public transit from either the Union Square or Fisherman's Wharf areas. (Check a Muni map.)

Getting to the Golden Gate Bridge would take longer using public transit, as it's a bit out of the way.