budget hotels Hong Kongvdo they exist

Suggest taking a look at www.booking.com and using its various filters (plus the map feature) to narrow your search...maybe with an assist from your nephew assuming that he's familiar with the city. A quick look is showing several hotels and hostels that would fit within your budget.
Hong Kong is a pretty expensive place, and cheaper accommodation can be found as you get further away from the city center, so orienting yourself with the map feature to find a place close to your nephew might be the driver for you.
The Kowloon side is quite nice, although staying over there would require daily commutes via the Star Ferry to reach the city proper - not an unpleasant option. It's been a few years since I was there but I don't recall that it was terribly expensive. Can google the ferry website to see whether the fares would make it worth your while.

Is that 125 Canadian dollars, or something else?

Have a look at the Salisbury YMCA Hotel.

The Star Ferry is free for everyone over 65, even visitors.