Rich, welcome into diving and Scubaboard.
I always prefer to have my training dives in places (or similar conditions) i intend to dive most. It is also good to face more difficult environments under guidance. I find that use of skills that were trained well, easy to transfer to less demanding waters.
Your first decision should be - how often you want to dive? If this will be one of the things you will plan couple of times a year when traveling for vacation, then having your checkout dives in warm water makes lots of sense. In Florida i would suggest heading to key Largo to John Pennekamp coral reef park. East coast Florida is more affected by Gulfstream and is fun when you are a bit more experienced to enjoy drift dives.
However if you desire to engage in diving more often, local diving is the way to go. Living in Chicago, Great Lakes are your local waters. We typically dive the Great Lakes from late April ro late October, local quarries even more than that. Another decision is what you are looking for underwater? Colorful reefs and prety fish is not what you will find here, there are many places around the world to offer that and that will be in warm water.
We have a very unique treasure here called shipwrecks, that offer a one of a kind experience. Preserved by cold fresh water, there are still intact wooden schonners over 150 years old, some with their masts still standing upright. Each one has a facinating story and many still carry artifacts from the times they sailed the Great Lakes. It is a unique maritime museum not found anywhere else. If you are a person fascinated by history, if you have a soul of an explorer, i can see you falling in love with Great Lakes diving
As for cold and comfort, you will need to dress for the occasion. I won’t be warm going skiing in 5 mil T-shirt so to truly enjoy local diving, dry suit is a way to go. Some local shops will rent you one and even will have your checkout dives combined with a drysuit training. Having this done locally, it will introduce you to equipment and techniques that are helful to explore shipwrecks safely for you and for the wrecks.
To give you a sense of what you can expect to see here, this is a two masted brig Northerner that sank in 1868 and is located 3 hours north of Chicago, near Port Washington WI. It is within recreational limits, 130 ft of warer, Though advanced cert and preferably deep diver training are needed to enjoy visiting it. There are other shallower wrecks that you can visit with OW cert.
Good luck with finishing your certification