I think acraven's suggestion of using booking.com as a search tool is sound.
The suggestion of Merchant City Inn by isn31c seems a good one. I can't speak to the quality of the hotel, but the location is good. I have fond memories of Virginia Street from my youth. The Virginia Galleries was a rickety Victorian structure home to many hip little stores selling records, comics, posters, clothing, etc. It was a great Saturday afternoon hangout in the early 90's. Virginia Street is also home to The Polo Lounge, arguably Glasgow's premier gay nightclub. They've been there for decades and there's pricey residential properties around, so I assume assume they keep the disturbance involved in having a nightclub on the street to a minimum.
From what I read, Mardee's suggestion of the Grasshopper's Hotel is good. In terms of accommodation, they seem to be the best value in the city centre right now. What I'm not so sure about is whether I'd like to be in that location for a vacation. I've been away from Glasgow and the west of Scotland for best part of 20 years and when I've gone back it seems Union Street has gone right downhill. I was astounded at how many vape shops one street can support. The corner of Gordon Street and Union Street is a bit edgy. I worked in McDonalds at the Argyle Street end of Union Street as a teenager and saw some stuff. It was quite rough even then. I'm not saying any of these things are dangerous to a tourist, but I'd rather be in the west end or merchant city if I was visiting Glasgow.
I don't have any particular recommendations for accommodation but here's a blank list of neighbourhoods that you may want to stay in that are within easy reach of the city centre:
Garnethill
Woodlands
Kelvinbridge
Kelvingrove
Finnieston
Hillhead
Dowanhill
Partick
Google some of those with your desired search terms and you may find somewhere.