The distance from Balmain to Parramatta is about 20-25km, so expect about half an hour travel time depending on traffic if you’re driving. By car, head down the city west link (depending where you are, it may be easier to go down Balmain Road or turn into it from Victoria Road), then onto Parramatta Road which will take you the rest of the way. Public transport really depends where home is. From the Town Hall Hotel, jump on the 441 bus to Town Hall and change here for a train to Parramatta. Does this help at all? If you let me know where you would like to leave from I can help with other routes.