We stayed downtown on the Riverwalk and already had a car for getting around and with a GPS had no trouble finding the place in about 30-40 minutes.
Buy your tickets online and then skip the ticket line on the way in. When we visited there were three lines for tickets. The two on the left were very long (stretching out into the sun) for people to buy tickets and then the one on the right had no line and was for people who bought their tickets online and just need to swap their "voucher" for their actual tickets. After seeing the line, I waited inside, bought the tickets on my iPhone and then used the short line to scan the barcode on my phone and get our paper tickets issued. Worked like a charm!
The caverns are very cool inside. There are numerous rooms (they get progressively bigger) and everything is artfully lit. Note I did not say "well-lit". It is very dim inside and you really have to feel around for your footing. They have put a path with a guard rail and a slip-resistant floor inside, but the place is soaking wet so you will slip a little here and there. For what its worth I didn't see anyone fall and even if you did you'd just fall down, you wouldn't fall over the side unless you were purposely leaning over the edge.
We took a 3 year old and a 6 year old. The 3 year old was a little scared but he did walk the whole way. Honestly it would have been more dangerous if I picked him up since I was more likely to slip than him and you really do need to keep a hand on the rail. We did hold his hand the whole way because he would easily fit under the rail. The six year old was safe, but slightly bored. I don't think they realize at that age how neat something like this is.
We went in May and with 99% humidity your shirt will be soaked by the time you get out and your calves may get a workout since the walkway is at about a 45 degree most of the time and the path is 3/4 mile long and the equivalent of 18 floors in elevation. There isn't a lot of steps, just steep inclined switchbacks pretty much the whole way.
We took the Discovery tour (they also have the Illuminations tour) which is a self-paced option. They have guides stationed periodically in the different rooms to say a few words about what you're looking at. All of them were kids (high school at most), most of them seemed very inexperienced and scared to death to be talking to a group, but they were trying and they did manage to get some interesting facts and tidbits out there.
Eat before hand! The food here is convenience store quality. Nachos, hot dogs, ICEE's, etc. and there is nothing nearby that I saw. Parking is very close so throw some drinks in a cooler for when you get out of the caves (you cant take any in) otherwise you're in for a $3 soda from the snack bar.
The caverns themselves are the attraction here and they are definitely worth seeing. You will not get a polished experience and amenities (i.e. food) like you might at a theme park, but this is not a day-trip, its a couple-of-hours trip and is worth it.