Anzac day has come and gone (25th April) so you've missed out on that one.
Games at the MCG
SATURDAY MAY 15 AEST
Richmond vs Western Bulldogs
MCG 2:10 PM
Both teams aren't going so well so far
SATURDAY MAY 22 AEST
Melbourne vs Kangaroos
MCG 2:10 PM AEST - depends on your flight
These teams are doing well and winning games so would be a good game
Otherwise you could go to Telstra Dome (also in Melbourne)
SATURDAY MAY 15 AEST
St Kilda vs Collingwood
Telstra Dome 7:10 PM AEST
St Kilda haven't lost yet (hoping they will this weekend), Collingwood has only won 1 game - should be a one sided affair
SUNDAY MAY 16 AEST
Kangaroos vs Port Adelaide
Telstra Dome 2:10 PM AEST
2 reasonable teams with good winning records - would be good
FRIDAY MAY 21 AEST
Collingwood vs Adelaide
Telstra Dome 7:40 PM AEST
Collingwood are crap - Adelaide isn't much better. But may turn out alright as they would be on the same playing level.
afl.com.au has all the stuff you need (rounds 8 and 9)
Hopefully a Melbourne Byoac'er can get to catch up with you. Or you could fly to the other side of the country and visit me

Cheers
-cdbrown