When transferring real estate as a gift, it does not receive a step-up basis, as it does when it has been inherited.

Since the properties are in New York you have a few extra steps you need to do to keep all of your funds out of NYs hands at closing.Here's an interesting BP thread on the South Carolina property tax issue you mentioned. https://www.biggerpockets.com/forums/725/topics/604427-south.... 

Any advice on other wise next steps?

What would be my first step?

Ideally, this would be just one step in a larger plan to grow into multiple rental units over time.

Where are your scheduled gross rents and effective rents so far in the last T12 months so we can figure out offense and defensive strategies.These would be the questions we'd go through in planning your steps ahead.

Joining BiggerPockets is a fantastic first step – it’s where so many great real estate journeys start.

Mortgage recasting is a great option for homeowners who:Have received a windfall, such as a bonus, inheritance, or proceeds from selling another property.Want to lower their monthly payments without extending their loan term or going through the hassle of refinancing.Are satisfied with their current interest rate and loan terms.How to Get StartedIf you’re considering mortgage recasting, here are the steps to take:Contact Your Lender: Ask if they offer mortgage recasting and confirm your loan’s eligibility.Determine the Lump Sum Amount: Decide how much you can afford to put toward your principal.Calculate Potential Savings: Use an online mortgage calculator or consult with your lender to estimate your new monthly payment and total savings.Submit the Request: Once you’ve made the lump sum payment, your lender will process the recasting and provide a new payment schedule.Final ThoughtsMortgage recasting can be a powerful tool for homeowners looking to reduce their monthly payments and save on interest without the cost and complexity of refinancing.

Front steps need redone.

You also need to take other steps (e.g. taking a look at the tax id number).I've seen mortgagees make various mistakes, but I can't say I've seen one in the area where the bank forgot to record the mortgage.