Lots of greyhound charities do this - the ones I volunteer for would do a homecheck with you, and invite you to meet a couple of potential dogs at, say, a regular walk, a store collection or for a walk with the foster carer at a local park.
Our local all breed rescues do similar - I'm particularly impessed by Four Paws Animal Rescue - they have monthly tea parties where you can go along and meet foster dogs and eat cake!!! 
Usually held in a hall or similar. Look up your local all breed rescues and see what events they have on. At this time of the year, foster dogs needing homes can be paraded during a fun dog show, can attend store collections,events etc - not a miserable kennel in sight. 
Also, you should bear in mind that virtually all dogs find the kennel environment quite stressful and it's very well known by rescues that you won't be seeing a dog's typical behaviour in this sort of environment. Hence, why all reputable rescues make such an effort to get dogs into foster care. Another one of our local rescues, Hope Rescue, has a policy of not rehoming dogs until they've completed at least fourteen days in a foster home - that's brilliant, and means the rescue will have a good understanding of the dog's behaviour and suitability for you.
I understand completely what you mean about finding them upsetting - one of our local pounds also has this effect on me - it's dire, very grim, very noisy, very dark. I hate it there. Local Dogs Trust though, has the most gorgeous kennels, quiet, well run, light and airy, with lots of facilities for the dogs. So it does depend a bit on where you are looking.