One of my favourite places to go for a drink and some food is The Brunswick Hotel. It’s in the Merchant City and beer/food is awesome. They also have a small hotel connected to it, which is doing deals at the moment for rooms (really cheap right now) and although relatively basic, is pretty nice. I’ve never stayed there, but I have been in the rooms.
The owners of the place are about as friendly and charismatic as you will meet, but the real selling point is the price/location and the awesome bar which is attached to the hotel! 😉 Brunswick Hotel
Alternatively, One Devonshire Gardens is doing some decent rooms prices at the moment (5* hotel, but pretty boutique considering it’s now owned by Hotel du Vin group). It will come in at the top end of your budget but is one of the nicest hotels in Glasgow.
Hotel Indigo is a pretty new hotel and is relatively small and very centrally located. It’s good value considering the standard. I stayed there a few weeks ago and it felt like it should have been in a higher price bracket.
Also try St Judes on Bath St, which only has a few rooms and is pretty nice. Only issue is, it’s right on the busy end of Bath St, so can be noisy at night.
You might also get a good deal on small serviced apartments at the moment, try 38 Bath St, I really liked staying there when I needed to get out of hotels for a while.