Conveniently located in Melbourne Central, just as you come out of the station, Hudsons has been my morning coffee stop on days that require bagels (at least once a week).
They charge $5.50 for my skinny cappuccino and plain bagel with cream cheese (seems pretty cheap, I'm guessing due to fierce local competition), and in return, I get heaven on earth - for a few minutes at least. They also have cheese bagels and blueberry bagels, but trust me, the plain ones are the best.
During peak periods (8–9am) there can be a disheartening line here, but you'll usually get fairly fast service anyway.
There are a few seats available (and heaps in Melbourne Central in general), but this is predominantly a take-away kind of coffee place.
This particular store has recently changed management – so far I've been overcharged and handed someone else's food – but I've been a newbie myself, so I'll give them another go.