After much searching, I've located at least one source that discusses the cost of refuelling and running the Falcon. According to the LucasBooks Star Wars RPG: Starships of the Galaxy sourcebook, refuelling a ship of the size and composition of the Falcon ("Collossal") would cost around 50 credits for sufficient fuel to last one day's travel which in turn equates to around 1kg of liquid metal.
The ship itself can carry a max of 60 days of consumables which implies that the main constraint on continuous travel is food, water and air rather than fuel (since 60 days fuel is enough to travel from one side of the galaxy to the other ten times over). Filling the tank to its fullest sensible level would therefore cost 3000 credits.
Refueling and Restocking
All ships must have fuel to operate; a ship without fuel is adrift and immobile, effectively disabled. In general, most starships refuel each time they put into port, and during refueling other essential ship consumables (such as water and oxygen) are restocked as well.
Refueling: For a starship of Colossal or smaller size, refilling one day's worth of fuel (approximately 1 kg of fuel) costs about 50 credits. Larger starships are substantially more expensive: Multiply the cost by 100 for every size category above Colossal. A starship uses this much fuel after one day of flight in realspace or hyperspace, after one hour of flight in atmosphere or combat, or in a single jump to lightspeed.
Restocking: Consumables cost about 10 credits x the number of living creatures on board x days of operation.
So the trip from Tatooine to Alderaan (and back) would cost Han Solo around four hundred credits worth of fuel (2 x jumps to hyperspace, 2 x days of travel, two atmospheric trips) and around a hundred credits worth of consumables to keep himself and his guests fed and watered.