As has already been mentioned, I guess it depends what your view of 'best' is. Are we talking diversity of species, breeding results, in-situ involvement, display technique? ZSL certainly has the most diverse public display and the ever increasing number of amphibian exhibits has to be seen as a good thing in light of the conservation crisis faced by that group of animals. My personal favourite is undoubtedly Chester both in terms of the species on display and the amount of work they do off show. Although I can understand the dissapointment if a percentage of the stock is not viewable, many of the species they are working with are rare or poorly studied so all credit to them for making the decision to try and breed them away from the public. My feelings are that most visitors will be more than happy if they can see a selection of species that includes venomous and large constricting snakes, large active lizards and brightly coloured frogs and in that respect Chester certainly delivers. Even for the herp enthusiast there's a lot to see - tuatara, caimen lizard, komodos, mallorcan midwife toads, heloderms, rhino vipers, phillipine crocs - many of which cant be seen anywhere else in the UK. Im in two minds about the increasing trend to distribute herps all over the zoo as part of a 'biome' approach. I can see why visitors may like it as it adds extra interest to other areas and avoids the monotony of tank after tank after tank of seemingly lifeless lizards and no-shows. Done well it can also illustrate an animals 'place' innature if you get what I mean.
I also like Bristols collection, particularly the style of their reptile house with the sloping pathways and planted borders. Paignton is another fave although ive yet to visit the new croc house. Durrell is an obvious choice,they do great work their with some incredible species. Im a big fan of Manchester Museum as well, especially with their involvement with neotropical frogs. Cotswolds renovated house is looking better than it has in a fair old while and Marwell are definately on the up. West Midlands and Colchester are worth a mention too.
Have to say im not a fan of Heythrop. Yes they've got a fair selection of species but there's nothing particularly out of the ordinary and as far as housing goes i'd have to say that its distinctly average. When I last went, they had a large monitor lizard in a viv that could barely turn around and several highly incompatible species sharing very cramped vivaria. They did say that new developments were planned however so hopefully things have now improved.
I'm sure that many other collections have got reasonable collections or exhibits but as has been mentioned, there does seem to be an increasing 'sameness' from one place to the next. I think herps get a pretty rough deal in most collections with standards for some being really quite shocking. A real shame as both amphibs and reptiles are in dire need of effective ex situ conservation, and, with a bit of thought, can make outstanding, popular exhibits.