We are also in the Chicago area and have found that St. Croix in the US Virgin Islands is a really nice Caribbean destination because it's a bit exotic and tropical but it is also a US territory, so that may make travel a bit easier.
There's lots to do topside on STX, great restaurants and water sports, and a wide range of dive experiences, including diving the Fredricksted Pier which is the best 30 foot dive I've ever done - and it would be wonderful for beginners!
We were there last October and we dived with St. Croix Ultimate Bluewater Adventure (SCUBA) and they were excellent. They have boats and shops on the North (Christiansted) and West (Fredricksted) sides of the island so you can enjoy a range of dive opportunities - shore, wall, drift, wreck, reef, night, pier, etc. We saw a wide range of sealife including seahorses, octopus, rays, reef sharks, and many more.
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One word of caution, SCUBA's west shore dive boat will be out of service from September 15th till October 6th (2021) for her biennial USCG dry dock inspection and painting, etc. so I wouldn't plan on diving with them during that period.
Take a look at the Christiansted Harbor Cam, STX is a great destination!
Official Page for Live St. Croix Web Cam | GoToStCroix.com