Water is water...bubbles are bubbles.... Especially for a new diver, pool time can me more valuable and less intimidating than local lake dives. After I was certified, the local community college in OKC had a platform diving pool that was 21 feet deep. For $5 they would open it one night a week for people to try out new gear, practice skills, or just blow some bubbles. I dove every week for several months. That opportunity not only made me a much better diver in the Caribbean or local lake, it got me past the relatively steep learning curve for new divers.
If there is a pool nearby that is open all winter long and will allow divers to practice, your problem is solved. Buoyance control is one of the hardest skills to master as a new diver.... and the best teacher is time under water. a pool is a great place to experiment with weights, work on buoyance skills, brush up on OW basic skills you may have had trouble with, etc.
You don't see sharks, lobsters, or octopus, or get your toes in sand...but hopefully you will find something close to home, and I promise if there is a dive pool somewhere, you WILL meet other divers. We're kind of a friendly bunch that love to talk diving. 99% are happy to help new divers and even though I showed up solo, I never had any problems finding a temporary buddy to dive with.
Welcome to the addiction, it will change your life for the better. There are also ways to dive cheaper than tropical vacations...and there are lots of ways to save on those as well. Southwest air will run specials to Florida (from DFW) for 130 round trip for cheap shore diving, Spirit has cheap flights to Cancun, and eating and sleeping in Cozumel can be cheaper than anywhere else....especially if you are single and don't require resort level accommodations.. I cant help with the getting time to go dive part, but it does not have to cost several thousand dollars to go diving. Taking a wife and kids with you....not so much!!
Good Luck,
Jay