Actually, at a continuous acceleration of 1G, you can build up some quite amazing speeds really quickly.
For example, accelerating at 1G (9.81 meters/second) for a period of one day (86400 seconds) will give you a velocity of nearly 850 kilometers per second. During this time, you will travel over 36.5 million kilometers.
A two-day trip, therefore, accelerating until halfway, and decelerating thereafter, would take you more than 73 million kilometers from your starting point. A four-day trip would cover nearly 300 million kilometers, or more than the typical length of a trip to Mars.
Basically, using a continuous acceleration/deceleration of 1G will enable you to get to anywhere in the Solar System in less than a month.
Hint, for the observer, you were much too optimistic but for the passenger, the news is much better than you wrote.
Then lets do it.