Have you considered looking to see if the universities offer virtual campus tours, or even looking on Google street view to see the area you'd be in? It's not just the campus that's important - you want to see the city you'll be in, and where you're likely to live in second/third year.
York's university (assuming you're talking about the University of) is quite far from the city itself, but is a fairly big, green campus. Birmingham's campus is similar, but the city itself has a very different vibe - much bigger than York. I don't really know much about Southampton or Bath.
From what you've said, Manchester might not be for you - it's very much a city-centre university, and whilst there is green space it's a lot more urban just because the uni is in the middle of the city. I wouldn't write it off entirely - you might find you like it - but if you're trying to shortlist a couple of places to visit, just based on what you've said, I'd prioritise the others.
I do really think visiting the places you're interested in is worthwhile though, even if it will be quite tiring and take you longer than would be ideal. It'll be home for the next three years, so you need to make sure you're comfortable with the environment.