Portsea Back Beach (and surrounds) on a hot, clear day is one of the nicest beaches I've ever seen, with the benefit of bay beaches 5 minutes away if you prefer that, this is only an hour or so from southeast suburbs of Melbourne, and minimal crowds and no traffic in peak summer.
In the city, I love cycling up and down the bayside trail. Sure you can't surf there, but to be able to the water and smell the salt on a bike path that can take you to the CBD, that's good enough to relax me. Lots of activities like kitesurfing, free beachside powered BBQs, etc make it a fun place when the weather is good enough. St Kilda beach is a happening place in summer with a lively boardwalk. Go further south on the path and check out Elwood for a quieter scenic environment. Continue on to Brighton Beach and check out the beach boxes. Keep going further and once you get to the Sandringham area the beaches become more rugged and ocean-like. On a clear sunny day it's really beautiful, water very blue and nice sand. Bonus: you face the sunset on Melbourne's bay beaches, which can be really nice, whereas the rest of the east coast of Australia only gets sunrises on the beaches.
Regarding internet - if you're in an area with cable, you can get cable internet which is 60mbit and fine. NBN is rolling out slowly which is 100mbit+ but mostly in newer developments for now. I could never do DSL. Mobile is good in the cities with Telstra usually ahead of US carriers in speed.
Unfortunately the climate outside of summer is kind of crap, relative to the rest of Australia, but the city is vibrant enough to offer other things to do in winter (which is not that cold, but the homes aren't built for winter and heating, and the sky gets gloomy a lot). On the plus side, you can take your vacations in the winter when it's summer in the northern hemisphere, or explore SE Asia where its warm year-round, or stay in Australia and check out Queensland or WA which are nice in winter.
In the city, I love cycling up and down the bayside trail. Sure you can't surf there, but to be able to the water and smell the salt on a bike path that can take you to the CBD, that's good enough to relax me. Lots of activities like kitesurfing, free beachside powered BBQs, etc make it a fun place when the weather is good enough. St Kilda beach is a happening place in summer with a lively boardwalk. Go further south on the path and check out Elwood for a quieter scenic environment. Continue on to Brighton Beach and check out the beach boxes. Keep going further and once you get to the Sandringham area the beaches become more rugged and ocean-like. On a clear sunny day it's really beautiful, water very blue and nice sand. Bonus: you face the sunset on Melbourne's bay beaches, which can be really nice, whereas the rest of the east coast of Australia only gets sunrises on the beaches.
Regarding internet - if you're in an area with cable, you can get cable internet which is 60mbit and fine. NBN is rolling out slowly which is 100mbit+ but mostly in newer developments for now. I could never do DSL. Mobile is good in the cities with Telstra usually ahead of US carriers in speed.
Unfortunately the climate outside of summer is kind of crap, relative to the rest of Australia, but the city is vibrant enough to offer other things to do in winter (which is not that cold, but the homes aren't built for winter and heating, and the sky gets gloomy a lot). On the plus side, you can take your vacations in the winter when it's summer in the northern hemisphere, or explore SE Asia where its warm year-round, or stay in Australia and check out Queensland or WA which are nice in winter.