I've found my post from pre season this year - and I've edited it to reflect this years draw.
This is the past 8 years. I've included this year's home/away games as one game - for obvious reasons.
It gets a little confusing with teams playing where - but I've included games where teams have played "basically" home games (Brisbane at the Gold Coast, Sydney at Blacktown, Hawthorn at York Park - because of their desire to play many more games there - as home games or away games played at home.)
Adelaide - 5 home games, 2 away games and 1 away game played at home 6-2
Brisbane - 2 home games, 1 home game played away, 4 away games and 1 away game played at home 3-5
Carlton - 5 home games, 3 away games 5-3
Collingwood - 3 home games, 1 home game played away, 3 away games and 1 away game played at home 4-4
Essendon - 1 home game, 2 home games played away, 2 away games and 3 away games played at home 4-4
Fremantle - 6 homes games, 1 away game and 1 away game played at home 7-1
Geelong - 5 home games, 2 away games and 1 away game played at home 6-2
Hawthorn - 6 home games, 1 away game and 1 away game played at home 7-1
Melbourne - 1 home game and 7 away games 1-7
North Melbourne - 4 home games played away, 2 away games and 2 away games played at home 2-6
Port Adelaide - 3 home games, 1 home game played away, 1 away game and 3 away games played at home 6-2
Richmond - 1 home game, 3 away games and 4 away games played at home 5-3
St Kilda - 3 home games, 1 home game played away, 2 away games and 2 away games played at home 5-3
Sydney - 3 home game, 2 away, 3 away game played at home 6-2
West Coast - 5 home games and 3 away games played at home 8-0
Western Bulldogs - 4 home games, 1 away game and 3 home games played away 4-4
Now the stats can be seen a few ways - Dogs' games in Darwin could possibly be called home games along with early St Kilda games in Tassie as well as North/Melbourne games in Canberra but I felt there was not enough footy played generally at these grounds and they were so far from their home that it should be classified as away.
Some analysis:
Western Australian teams have played 1 away game between them.
North have not had a home game in Melbourne but have played 2 all up.
It's a pretty rough guide - don't take it 100% as gospel, but it certainly shows that we have been absolutely shafted.
Melbourne has had the fewest matches in their home city of any team.