I have always camped in the back country when staying in that area. I would certainly choose Glacier rather than driving to and from Bellingham. Hopefully others will,pipe in about places to stay as your choices will be limited in Glacier and I can not give recommendations. I used to love eating at Graham’s although I have not stopped there in ages.
If you end up staying in Bellingham, check out hikes on/around Chuckanut Mountain. Unless you want to hike in the Mt. Baker area, I’d stay in B’ham.
Glacier. There are some truly world-class hikes in the Mount Baker area, and you'll be closer to them in glacier then you would be in Bellingham.
It depends what type of lodging you are looking for. Glacier is a tiny mountain community with no hotels, only rental homes and a few restaurants. Bellingham has a full range of hotel options, restaurants, breweries, events, activities, etc. Glacier is in the mountains. Bellingham is on the water.
I would opt for Glacier, just to be closer to the trails. We have stayed at the Blue T Lodge there and were pleasantly surprised. We were not expecting much at all, just a room for a night, but it was quite nice. The restaurant next door, Chair 9, was good also. We have been there many times though so knew what to expect there. Anyway, this is a good spot to stay for being close to good hiking.
Take Mtngrl advise if she recommends a place in Glacier and you can get a room. You will be close to some spectacular scenery.