Hey, don't know if you've already made a decision, but Sydney is the scientific research capital, closely followed by Melbourne, both have institutes with good lab facilities etc. This might limit where you can go with your grant. Try the Garvan Institute in sydney.
As for which city to go to: Sydney is good if you stay near-ish to the coast. It gets real hot in summer inland, and the roads are chaos getting to the beach if you're in the western suburbs. Look at northern beaches, eastern suburbs, or sutherland shire. Almost everyone in these areas surfs, and it's crowded on weekends (I have trouble finding a quiet place to learn the basics of surfing). Plus, if you take a weekend trip away, you have hundreds (yes hundreds) of surf beaches and reefs within 2 hours up or down the coast from sydney.
Never been to melbourne, but they get some really hot days (42C) followed by cold days all year... the weather's a bit unpredictable, and it rains more than in sydney. On the other hand, they get a lot more wind from the southern ocean, and with the wind there comes 4-6m swell

too extreme for me, but it's common in that part of the world. I'm not sure about this, but I think you have to drive further to get to surf beaches in melbourne, but there's plenty of coastline around there so surfing shouldn't be a problem.
P.S. I'm an immunologist researching transplantation in sydney at the Red Cross. Let me know how you get on with the grant.
Hope this helps,
James.