The easiest way to get where things are happening is to jump of the airport bus by korsvagen. Here you are near the Swedish fair, hotel Gothia and Liseberg.
A service I recommend is using resrobot(travel robot) you see here>>>. With this one you just write the goal you get the quickest way going somewhere in Sweden.
Airports in Gothenburg
At the moment just one for commercial flights
Bus in Gothenburg
Another affordable way to get around in Gothenburg
Way traffic cameras in and around Gothenburg
Some cameras on the roads in and around Gothenburg.