Ask for a sample menu, routine, what kind of activities they do. Check out what space they have to play in, including the outdoor space. Are there any concerns eg I've seen garden space next to public footpath with low fence where kids were chatting to passers by unsupervised!
I think you can tell a lot just by the atmosphere of the place - at my DS's nursery they greet you with a big smile, always say hello to the children by name. The staff are always down with the children (as in sitting/kneeling at their eye level, interacting with them). They're welcoming and engage them in conversation as soon as the children arrive. They have a great food policy, v healthy and fresh, they plant veg and herbs with the children to use in the kitchen. They also go the extra mile - parent breakfasts every so often, where they give you breakfast to take away after morning drop off!
Make sure you know all the practical stuff - opening hours, how you can pay your bill. Think about how opening hours will fit in with your needs eg to account for commute. Ask how soon you need to book a space and find out what days they have spaces so that you can begin to plan your working week/other childcare.
Ask how they let the children sleep - first nursery I used had really tiny rooms and DS struggled to sleep there as he had to sleep in a cot in a small noisy baby room. His current nursery blacks out a separate room, put mats and blankets out for all the children to nap together. If any wake up early they go next door to play.
Ask for a recent newsletter if they have one.
A great nursery will give you most of this information without you having to ask!
Try to visit a few nurseries to get a feel for what you do/don't like.