Hi! I recently went to Beijing in the end of July for the start of a tour.
I stayed in a hotel for a couple nights quite close to Tiananmen square. It's about a 10 minutes walk up the street. I could see the Forbidden city from my window there, although it was still a bit off in the distance. I walked back from the Forbidden city, through Tiananmen square and back to our hotel as part of the tour.
The name is the "King's Joy Hotel Beijing", 81 Meishi Jie, Xuan Wu District. I took a taxi there from the airport, although the driver needed to call the hotel to figure out where it was. It's probably a lesser-known accomodation in the area but was still very nice! My friend thought the bed's weren't so soft, although I had no problem sleeping. Overall it was very clean with friendly staff. Look it up online and see if it's the type of place your mom and her friend are looking for!