We visited Huddersfield two years ago, OP on an Open Day.
It had been rising up overall league tables and getting good reviews and has TEF Gold for teaching. It has had a little dip in the last couple of years league table wise but so have many places. It was a uni with a real sense of PR, I felt. We also visited NTU, Hull, Lincoln and OBU and would have rated Hud below all of those but that was mainly on the place to be honest (and geographical accessibilty for us). Huddersfield as a town is nothing special (nice scenery though)
Of DS's friends who went to uni (actually not very many) the only one who dropped out dropped out of Keele (also politics but he dropped out before any teaching occurred) . Although that may be more to do with his anxiety at uni than Keele itself. He is now at Lincoln and managing fine.
Keele is definitely a place if campus is your major preference. Other campus unis (eg UEA) are near large towns or cities. Keele really isn't so can seem isolated both when in it and to get away from for day trips/visits home. Might be OK if the student drives and has a car I guess.
On the face of it, Keele may have the better reputation, but I know students who have got into Keele in the last few years having got very low A Level grades (I think it does find it harder to attract recruits than some other unis because of its isolation and students not being able to pin a location to it) but not Huddersfield which, by the way, has a top reputation for music as an aside!
All that said, Keele has regularly been named as one of the unis with the highest student satisfaction ratings. When DS's friend dropped out he was treated very well by Keele who tried to help and actually offered him the option to hold his place for a year.
Of the three, for politics specifically, I would say not Coventry which is very good for some specific subjects. Coventry also has a high proportion of students who live at home so may be harder to settle for someone who doesn't.