I have an early 90s Miele road bike with a 6-speed freewheel casette. When putting on a new tire to use on my trainer, I noticed the wheel's rim is completely cracked. Can I buy a new wheel that I can move the 6-speed freewheel casette onto? All I can seem to find are wheels that are compatible with freehubs, not freewheels.

I also wondered if it's an option to buy a new wheel that uses a freehub. and by a 6-speed freehub casette, but I can't seem to find any. Is this even an option?

Freehubs and cassettes were never widely produced in 6-speed. I think that your best (cheapest) option is to buy a new wheel that is freewheel compatible.
Here's an example. I'm not sure of the quality, but it will work as long as your current rims are 700c.

You could, of course, have a new rim and new spokes relaced to your current hub.

Frewheel-type hubs and complete wheels are still available but are considered obsolete so you won't find them everywhere. Try an older, well established bike shop. They might have one still in stock they would be happy to sell at an attractive price.

6-speed and 7-speed hubs are the same overall width (126 mm OLD) so any 7-speed freehub based wheel will fit your frame and 7-speed cassettes are still readily available to fit modern hubs. Assuming your shifters are friction, they will work with any 7-speed cassette.

Might? We sell more freewheel wheels then freehub wheels. Of course, our store is more of a community, recreational rider store than the higher end racing store. We get a lot of repairs for destroyed freewheel wheels where the owner doesn't want to buy a new wheel and cassette, shifters, etc. They just want a new, decent rear wheel.

But, yeah, if you like your rear hub, just swap a new rim onto the old hub and spokes, if the spokes are of correct length. If not, you can get new spokes also.

The less boutique like stores can easily get you a replacement freewheel compatible wheel that they can then take off your present freewheel and put it onto the new wheel. Or if you have the tool and a BIG vise you can do it yourself.

Great feedback, thanks guys! I'll take it in to my lbs and see if they have any compatible wheels.

buying a replacement wheel is likely cheaper ($35 as cuevélo linked above) and much less work than putting a replacement rim (and possibly spokes) on the old hub. You can barely find a low-end rim for $35 these days, let alone new spokes (probably another $25).
Although building wheels is fun if you want to try it.

Your store is probably an exception. Where are you located?

These days all mid and higher line race, sports, hybrid and mountain bikes use freehubs and cassettes. Even Trek's lowest level "Bike Path" model has a freehub.

The only freewheel bikes I've come across are Department store level stuff and, of course, much older bikes that are being resurected after years of inactivity.

I had a crack on my rear wheel for about six years. I kept a close eye on it to make sure it wasn't getting any worse. I finally took it it to the LBS a couple of months ago and had them build a new wheel using my hub - cost me around $100,