While travelling you might not bring a bike, but in case you do, Manchester has a bike cafe, Pop-Up Bikes. Based in one of the arches under the railway line out to Leeds (I think) you can bring your bike in there with you, and they offer bike parking, you can leave it safe and dry while you explore the city.
Say something happened to your bike they will fix it that day or try to, they have always managed this for me.
Even if you’re without a bike it’s a nice place to have a cup of coffee and I can safely say that Pop-up bikes is one of the least pretentious coffee shops in the city. They tolerate pretty regular invasions by me and my son. We are both the kind of people who are hard on things and I need repairs often. On days when I’m on my own I can quietly sit in the corner for hours drawing or writing, it’s that kind of place.