I've been living in SYD for about 5 months now. What time of year will you be here? I think Sydney is probably a 3-4 day city, but coming from the US, you may want 1 extra day due to jetlag.
Harbor Bridge walk - seems overrated to me, personally. Seeing a show or something at Opera House could be fun if you're into that sort of thing
Opera Bar area is a fun & lively place to get a drink and meet people. For the Ferry, recommend the Manly Ferry - probably the best views.
Snorkeling/Diving isn't really SYD, you'd need to go up to Port Douglas & the reef area. I haven't been to Port Douglas yet, but hoping to get up that way soon & check out Daintree as well (and the reef, of course) - I've been told by coworkers that if you want to do the reef right, take a helicopter out one-way, spend the day diving/snorkeling, and a boat back (or vice versa) as it's a great way to experience the reef.
As for Melbourne - personally, I wish our offices were located there as I like MEL much more as a city than SYD (I live in Darlinghurst in SYD) - it's got more culture and feel to it than SYD does. I'd personally spend more time down there if not doing the reef and maybe just 1-2 days in SYD (and honestly, I'd personally skip SYD and do MEL & the reef - but that's just me!)