My first answer is Commercial caves.
As was stated in the Buckners thread (It's probably one of the best choices in the state right now) its kinda lean for wild caving. Public land is closed.
There are plenty of novice caves available on private land....and nobody is likely to just list them for you. First, that won't help you much without locations which they aren't likely to share with a stranger. Caves require not just finding out the location, but also mainting good landowner relations. In short, you need (as you have been told) to make contact with one of the local grottoes like the CIG, HCG, etc...and get involved in the caving community and the people who have the information, and more importantly the context. As an example, some caves that are good for novices have bad landowner situations, can flood in wet weather, or can be confused with other nearby caves that are not suitable for beginners.
As a case in point, The SJVG grotto (Northern Indiana) just did a trip to Clicks Cave in S. Indiana on Saturday. The cave is gated and requires a key. It's also a decent cave for all but very young cavers. Had you called each of the grottoes listed for Indiana or even just the CIG they might told you about the trip. It's unlikely another trip will be scheduled real soon with the elderly landowner since we don't want to wear out our welcome at such a nice and well known cave.
I'm not trying to be hard on you, but time after time people come here, ask about caves, we tell them what to do, and they refuse to believe that some cave fairy won't just wave a wand and let them skip making contact with local cavers and earning their trust.
I'm not scared of the dark, it's the things IN the dark that make me nervous. :)