Only too happy to help. I live in Adelaide. I don't know your location but judging from the post you're not from Australia I think.
It's not a big city in population terms (about 1 m.) and its topography is linear (north-south). The metropolitan area (we use the term "Adelaide" in a familiar manner, not a technical one and we use it to cover all of the metro area).
The metropolitan area has a coastline its entire length. If you are looking for what we would call a "beachside suburb" then you have much to choose from. You've indicated Glenelg, yes, nice suburb.
Others on the beach which are good are
Glenelg North (use the tram)
West Beach (bus)
Brighton (train or bus)
Seacliff (bus)
Seacliff Park (bus)
Henley Beach (bus)
Grange (bus and a train but don't rely on the train)
Largs (bus and train)
There are more.
A useful website is
http://www.realestate.com.au (click on SA). Prices vary so I won't try to pronounce on that.
Public transportation into the city varies. From Glenelg you have the Bay Tram as we call it
http://www.adelaidemetro.com.au/guides/glenelg2.html
It's old, it rattles, it's noisy, we love it
Some useful websites:
http://www.adelaidemetro.com.au/index.html
http://www.sacentral.com.au/site/page.cfm
April is cool and changeable. It can be showery and we even have some constant rain so bring appropriate clothing.
The State itself is bigger than the British Isles but our population is only about 1.75 million. SA Central has lots of info.
Any other questions please ask.