Photography wise I'd say it's possible to get good photos at any zoo, but some are easier than others, either because they offer unobstructed views, painted fences, or there are positions that are easy to focus beyond the fence / avoid direct light or they have glass you can get straight onto that isn't scratched. It can depend on what lens you have. Something to consider is what you want to fill the frame with (a short lens is good at a large enclosure for animal plus atmosphere but it may not be as good for a close up, a long lens might give you great close ups but no range, if you have a zoom you can do both but it's always worth thinking about how long the long end is).
Then, are you mainly concentrating on small animals or large ones, do you want animals moving or stationary, are you going for record shots or will you treat it like a wildlife day and wait ages for the animal of your choice to do a thing or is it anything will do as long as it's good.
Some of my highlights / recommendations would be these. I can't really comment on signs though they all seem fine and informative to me. I shoot full frame so any lens comments are based on that.
Chester - this is a great zoo for photography and as well as good open views of large animals , it has some of the best views for free flying birds. I'd recommend mid week if you want to hang around in one place for a while as it's a little less busy and people won't run buggies into you as much. I take 420mm fixed or a 100-400 / 150-500mm zoom. Longer is nicer for something like the Orangs.
Whipsnade - as well as excellent all round views, great backdrops and enclosures and the opportunity to get close and near shots, also has the excellent bird show if you like birds in flight. I take my 600mm birding lens (or 200-600) as long isn't an issue here. But you'd have fun with anything. While this is my local it's one of the best places in the country in my view.
CWP - great collection, amazing backdrop, a lovely tropical house (again if you like birds this is like a Xmas present photography wise) and a few challenging spaces but photography is fun and enjoyable at most enclosures. And you can get some plants if you like that too. Something up to 400mm will work, a zoom will be flexible and cater for all the smaller spaces.
Hawk Conservancy - a bit left field zoo wise I guess but small but well formed and I really recommend one of their photo days, if you are a bird fan. I think visiting on a regular day and going to the flight displays would be fun anyway though. Lovely birds, good spaces, 100-400mm was my lens of choice for that.
YWP - great unobstructed views, excellent variety of animals and after all who doesn't want to photograph polar bears playing with canoes in the water. 600mm is my lens for a day there but be mindful of the walking distance if you want to take weight.
Trentham monkey forest - if you like macaques and enjoy photography this is a great place to visit. You can wander around spend as much time as you like and sit around on the benches watching the behaviour to get the right shots (and enjoy the primates of course). Bit niche for some I expect, but excellent in my view. Zoom with a long end but some 'wider' shots are amply rewarded here.
From that list I think it's obvious you can choose what you like really!
Also working for photography and fun to visit though
- Dudley - good angles and the castle to play about with in images
- Slimbridge - has captives (though not really my thing when I go there) and you can fit in some wild things too, same Arundel
- Bristol - in the bear season, you can get some amazing views and shots of the wolves, bears, wolverines and lynx and the cheetahs have a great enclosure for pictures. The wood area is the highlight for me though and it's a real wow
- Hamerton - for the collection and some good photos spots for unusual animals like the lovely Corsac foxes
- British wildlife centre - do a wonderful photo day which includes red squirrels (if they want to come out) and Reds can also be had at Peak Wildlife park which has good angles and some more Polar bears to boot.
