Lesley, I went to Chester for the 1st time ever last Monday and thought much of it was brilliant.
We got there 1st thing and went straight to the Realm of the Red Ape where the orangutans are housed. You see their indoor areas from inside the main building and there are also viewing windows inside onto the outdoor areas if you see what I mean (otherwise, as far as I could see the only way of seeing them outside was at the foot of the area where the waterfall is). This worked really well for us because for a while me and my family were the only ones in the building and were therefore treated to an unobstructed view of the orangs (and plenty of photo opportunities). We went back to RORA twice more - in the early afternoon it was jam-packed, and very noisy, but right at the end of the day, there was only a few visitors.
Needless to say seeing the Sumatran orangs was a real wow, though the Bornean group were nowhere to be seen and a keeper explained that there are some off-view areas (i.e. the old house) where they often tend to go.
We also spent a long time watching 4 elephants playing in their pool in the afternoon around 3-ish, which was delightful, so it may be worth visiting them at about the same time as I think (from other people's reactions) that this is quite a common occurence.
I was also very impressed with the jaguar exhibit which is close to RORA, and had no difficulty seeing them in the middle of the day.
Never having been before we kind of ambled about a bit aimlessly and certainly went round and round in circles somewhat ........ but later, having left at 6, we found that we'd missed only a few exhibits right on the periphery of the zoo ....... namely kangaroos and zebras. Ironically, my other half had been remarking that you don't often see kangaroos in UK zoos (wallabies yes ...).
I hope you enjoy it - I definitely want to go back, but my main tip is that if you want to see the orangs in particular, get there when it opens and go straight there ............ in main entrance, left over the elephant bridge and then veer left past the warty pig and chimps (who are also fascinating, but don't stop as there is lots of outdoor viewing, you can come back to them at any time ...... we managed to pass by the chimps 3 or 4 times during the day and there was something to see on the island each time, though their indoor area was a bit crowded a round midday admittedly).
I also really enjoyed the twilight zone - which I think I've read somewhere is the largest bat zoo display in Europe (if not the world). Once your eyes adjust there are loads of them.