“Do you think this will go well in the study?”
You're shopping for furniture with your fiance. You find a desk that you like, but you want to get his opinion on whether it will fit with the other furniture in your study. You point to the desk and ask this.
Do you think this will go well in the study?
Use "will" to ask for someone's prediction about something in the future. In the example above, you're asking your fiance to predict how a piece of furniture will look next to other furniture in a room. So "will" is the correct word to use, not "going to" or any other future tense words.
When something "goes well in" a room, it means that it looks good in that room. The colors and style match the other objects and the overall look of the room.
"Go well" can also be used in the phrase "go well with". This is used for asking about whether two items, such as two pieces of clothing, look good together:
That jacket doesn't really go well with those shoes, dear.
Even more casually, people sometime use "go with" in the same way:
That jacket doesn't really go with those shoes.
"The study" is the name for a room in some houses. It's a room where people keep books, a desk, and maybe a chair for reading in. It's similar to an "office", but a home office sounds like a place where family members are doing some kind of actual work. A "study" sounds more like a luxury.