The figure of $200 a month sounds right to me. Of course, you won't spend it every month, but some months you will spend more if you've got a vet bill in there, even if it's a routine dental, physical, etc.
It's best to think of it as an annual expense and $2,400 a year is right in the middle according to this chart.
The Cost of Owning a Dog
When your puppy is young the bills aren't that bad, but as they age they can rack up the vet bills. At age 14, Lady costs me about $5,000 a year just in medications, routine exams, bloodwork, etc. Food, emergencies, etc. are all on top of that.
One bout of pancreatitis requiring hospitalization can easily result in a $1500 vet bill. You absolutely need money set aside in a separate account for emergencies. ER vets require payment upfront and they will turn you away if you can't pay.
Our Health and Sick sections are full of posts from desperate owners faced with unexpected vet bills they don't have the funds for.
I know moving seems like a long way off, but remember that you will hopefully have your Yorkie for 15 years. Finding pet friendly housing can be challenging in some areas of the country.
Yorkies are notoriously difficult to housebreak.
I am very glad you found YT. Spend some time here and read, read, read. You'll get a good idea of what Yorkie ownership is like, the pros and the cons.
It's good you and your BF are discussing this beforehand. It's important for all family members to be on board when adding a pet to the family. Pet ownership is wonderful, but it also requires work and commitment.