Don't know anything about the Day's Inn.
The airport and the Day's Inn are actually pretty close to the area where you'd find "down home" Cuban food. But not walking distance. And the restaurants aren't in places that are great to walk around. To minimize cab fares - I'd suggest just taking a cab to south Beach - strolling around - finding a restaurant - and eating there.
Cuban food is not in general a "distinguished" cuisine - so it's not like you'd get terrible food at one place - and a really great meal at another. Chances are you'll wind up with a middle-of-the-road meal no matter where you eat if you have Cuban food.
If you only have one meal in the Miami area - and are up for a splurge - I'd definitely suggest going to Joe's Stone Crabs on south Beach. The specialty is - of course - stone crabs. And if you like crabs - you will love these. Also - they are a very regional item. You can find them in restaurants outside south Florida - but they don't travel well. I live in north Florida - and won't touch a stone crab north of Palm Beach. Joe's is *the* stone crab restaurant in south Florida. It is probably over-hyped - over-priced and over-crowded (although if you hit it late - but not too late because it closes at 10 - you can probably avoid a very long wait). But - because of the huge volume it does - you will always get the best crabs available. It is reasonably close to the action in south Beach. So you could take a cab to Joe's - eat - and then spend a couple of hours walking around. Robyn