I second what others have said about holding off until after the pandemic.
In the January to February weeks you mentioned, your biggest issue is going to be weather. I'm forced to take off two weeks from work during the first quarter. In the past, 3 years, I have done a week long tour with Adventure Cycling in Southern Arizona, departing from and ending in Tucson. Amazing, perfect weather and the right amount of flats and hills. This wasn't a free trip but you get your money's worth with the support, the hotels and the meals.
I've also done a week-long tour in Key West in Florida, this one being the most recent and enjoyed it very much. The group that I rode with does it every year. If you are interested, PM me and I'll connect you with the leader. You pay for your hotels and your meals and the group rides together at a nice pace. It's 99% flat and I'm thinking of doing it again, after COVID. Flying in and out of Miami, FL.
I also did New Orleans years ago and loved it. My buddy and I rented a vacation rental for 5 or 6 days and just went on rides everyday. The food was amazing. Another choice is also Austin, Texas, which I'll do again for the BBQ alone. Those briskets.......