It’s not even that noisy in my opinion unless you get one of those inward facing courtyard rooms where it just echos. If you think it’s noisy, you just don’t like downtown noises I would say.

Also the GH isn’t “that” far of a walk to the Gas Lamp. 10-15min maybe? I haven’t done it since 2019 but when I had 200 nights in San Diego split about 50/50 between the two, it didn’t seem like a big deal.