The only options I have found are to first set the Scale tool on the Tools toolbar to the desired scale you want before using the Go to XY tool and then only use the Pan To tool rather than the Zoom To tool, or else use the Zoom To tool and let it zoom to the extent it wants and then enter the scale you want into the Scale tool on the Tools toolbar. Both of these options keep the coordinate you entered in the center of the screen and result in a scale that you can control to the desired level. The Pan To option is the best since you only have to set the scale once if keep using the Pan To tool and you don't have to constantly reenter the scale after panning to each coordinate, and the Pan To behavior is the default when you press the enter button after changing the coordinates of the tool. With the Zoom To tool you always have to override the scale after finding each coordinate.
The help for the Go to XY tool has nothing that indicates it is possible to change the Zoom To button behavior of the Go to XY tool. I tried changing the Data Frame Extent setting to use the Set Scale option, but then the Zoom To tool is disabled and you cannot change the scale of the map at all. Changing the Reference Scale of the Data Frame had no effect on the Go to XY tool either.
Changing a layer's "Don't show layer when zoomed: Out Beyond (minimum scale)" setting had no effect on the Go to XY tool behavior.
No solution to control the scale used by the Zoom To tool came up on any of the Tips and Tricks of the Go to XY tool I found online, suggesting no one has a real solution that avoids a two step process.
I programmed my own coordinate locating tool using VB.Net, but I only bothered to design it to use the normal spatial reference of my data, and it has no other options other than to let the user control the scale the tool will use. Replicating a tool identical to the Go To XY tool is something I could do if I wanted to, but I have instead designed other tools that find locations based on other datasets that all my users rely on to get around. If I recreated the tool the only change I would make to its design is to add a number box on the tool that would let you enter whatever desired scale value you wanted the tool to use by default to control the Zoom To tool behavior, so that you could set the scale once and forget it and easily see what the current scale setting was if you did not like the scale the tool was using.
I will add that suggestion to the Ideas site. With a number box on the tool controlling the scale they can initiate the tool to show the standard scale they currently are using and store the last user preference entered into the number box in the Registry so that the user only had to specify their preference once and forget it. Alternatively, they could configure it to set a default option added to the General Tab of the Data Frame to let you customize it for each map, but then you would need a help document to tell you where to go any time you wanted to make an adjustment to that setting. Anyway, user control of this behavior is a no brainer, since only the user should decide what scales work best for their workflows, not a lazy Esri programmer that did not even bother to consider that possibility.
