Wont answer all the questions but I'll answer some from my point of view.
Weather - You will get used to the weather very quickly in Melbourne. It's not half as bad as people think. Also bear in mind it doesn't rain all that much (Perth gets more rain than Melbourne), it drizzles. Which means you can still go out and do stuff, and the funny thing about Melbourne is people actually do. One little sprinkle in Perth and the whole city comes to a complete close. Melburnians have learnt to live with a little strange weather and you will find heaps to do in all seasons.
Renting - Try the south east suburbs (Glen Iris, Malvern areas) or yes you can head to the North as you have stated. You really can't go wrong as long as you stay away from the West (only until you know Melbourne better). Also you will be pleasantly surprised for what you get for your dollar in Melbourne versus Perth.
Beaches - Perth wins on beaches (as in the actual beach) close to the city. However does Perth have the infrastructure on the beaches like Melbourne does? No, because local city councils never allow it. So if you just want to take a stroll down the beach, grab some CHEAP fish and chips and watch the water Melbourne is your place.
Outdoors - HANDS DOWN Victoria destroys WA for outdoor living, and the best part is it's all seasons in Victoria. Kayak on the Bay, the Yarra, take a drive up to Albury (3.5 hours away) and Kayak on the Murray or Lake Hume, the best part is in you'll be in NSW (OMG another state!). Cycling, Melbourne takes the cake for bike paths. Also the cycling culture is very very strong in Melbourne, many major roads have designated cycle paths and cars don't drive like morons around bikes like they do in Perth. Walking in Melbourne is the best, especially hiking. Melbourne actually has things to climb UP if you are interested, and you don't have to drive 7 hours to Bluff knoll to see some actual height, also Melbourne is green, not brown.
More on outdoors - Melbourne has a ski season, even if you are not into skiing, strap on a pair of snow shoes and walk around Lake Mountain, it is stunning.
Like visiting those small country towns or cities without feeling like you are about to abducted and murdered by the locals? Victoria is your place, Daylesford, Bendigo, Sale, Torquay, Lorne, the list goes on and on, and they all actually enjoy and welcome the tourists.
Travel times to work - Okay good and bad points here. Bad points, yes Melbourne traffic can be pretty bad, but you seem to be looking at areas close to the city and the tram system in Melbourne is awesome. I used to live in an inner city suburb and trust me you will opt for the tram over a car. Which brings me to my next point, As spread out as Melbourne is, it's not as bad as Perth and we have more than just one road into the city so at least you won't be stuck out on the freeway/highway 50 kms from the city.
Other good things about Melbourne - Proximity the other cities, you can leave Melbourne airport at 9:00am, and be in Sydney central station by 11:00am, and it's bloody cheap.
Also don't buy into this crap about cheap flights to Asia from Perth. Other than the few SE asian countries, the increase of traffic from the Eastern states brings prices to the same if not lower than Perth. There is more to Asia than Bali and Phi Phi island.
Development, at present Perth is seeing decent amount of development in the city, but wait until you hit the East. Melbourne just put in a 6 story mall in the city without a bat of an eye lid (I heard about it maybe 2 years ago), I am still waiting for Elizabeth Quay to be built since hearing about the latest approved plan 7 YEARS AGO! I'm pretty sure that almost the entire district of Docklands has gone up in that time.
Things to do - Shows, sport, festivals, art, music whatever you want, Melbourne has it.
Coffee - Yes the coffee is better in Melbourne (just joking………………… but seriously yeah it is).
Anyway I may seem biased and yes I do love Perth but I'm sorry Melbourne is so much better. Keep your house in Perth, try out Melbourne for some time and see for yourself.
BTW I will hopefully be beating you there as I plan to move back (well somewhere in the east) before the end of the year. So keep this thread updated as I would be interested to read up on how you go.
Experience - Lived in Perth for 20 years, Lived in Melbourne for 6 years.