We recently stayed at this apartment as we were going to the excellent Celtic Connections at City Halls. Fraser suites have studio, one bedroom and two bedroom apartments, with continental breakfast if you want it and is very centrally located at the bottom of Albion St near Argyle St.
We booked a studio apartment and did not expect it to be as plush as it was for the price ( £67) . The room was huge and had a great king size comfortable bed, a double sofa, flat screen TV and surprisingly well equipped kitchen with both microwave and hob and plenty of pans etc. There was also a table with two chairs and the bathroom was well appointed and with L’Occitan toiletries. We were both impressed and comfortable, the only downside was the noisy students outside at 3.00am in the morning, the price you pay for city centre I guess.