Question first! Where are you coming from? (from your spelling, I'd guess US - or perhaps you made some allowance for this being a US-based board!)
Then answers - of sorts:
1. Less lower north shore is a good neighbourhood, and yes - you will pay over the odds to live there.
Depending on where you end up working, you may find cheaper suitable places. It all depends on what you want.
2. Running and/or cycling to work is not common, but it is possible. Again it depends on where you live and work. In summer, which is pretty humid, you may be quite unpopular, unless you pay particular attention to personal hygiene.
3. $80K-$100K is a better than average salary for Sydney. But then, Sydney is an expensive place to live! Pretty interesting, challenging, exciting, though.
More info from you may get a more precise or intelligent response from me -but no guarantees on that second qualifier, though! - come to think of it - no guarantees on the first, either. MAY is probably the most important word in that sentence!