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.
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.