Parking your car for the night in Geneva might jsut make the trains look a little better - OR get your car on the day you leave Geneva (you will get a free transit pass from the airport into town and then from your hotel for the 24hours you are staying there... so no additional costs in the city and canton of Geneva.
Places to visit from Geneva en route to Zug - there are many. I would opt for Bern. An easy drive from Geneva and then on to Zug- Lots to see and since the town is small a stop of 4 hours is plenty including time for a light lunch. See this:
If you prefer not to stop in a town, but to drive through the mountains, here is a possible route:
Geneva to Aigle (autoroute via Montreux)
From Aigle up through the vineyards and over the Pillon Pass
Then from there over the Brünig pass to Luzern
And on to Zug
A lovely day's drive with many (too many!) things to stop and see along the way. If this appeals to you tell me and I will provide more details!!