Parking recommendations

We have an upcoming 2 night stay in NOLA while on our cross country road trip. Our car is full of all of our belongings and we’ll take some of it into our lodging with us but we can’t take in everything. The place we’re staying recommended the Gordon lot as it’s nearby but we’re thinking about maybe using the Fulton parking garage for added security and peace of mind. We’re open to other lots too, just looking for any and all advice :) Thanks in advance!