Phillipsburg is a hike from Divi...maybe 20 minutes or so. Not too bad. I've done it many a time, but I do agree that you should rent a car if you can possibly swing it. That being said, where's what to do if you can't swing renting a car.
You've got to get a Taxi from the airport to Divi, right?
On the way in to Divi, you'll go through a town called Cole Bay. Right across the street from the Daihatsu car dealership there there is a market called the Lido. They have take out BBQ which can't be beat. Have your taxi driver stop there and pick up 4 or 6 meals to go, all wrapped up, and bring them to Divi with you. It's about 6 bucks per meal, and some of the best BBQ you will ever have, anywhere, bar none. The place is right on your way from the airport to Divi. Get take-out, and heat it up in your room at Divi. Trust me, you'll enjoy sitting on your balcony at Divi eating BBQ from Lido. You won't do any better than this, no matter how much you spend.
Cheap eats within a 30 minute hike from Divi?
As you go down the hill into Pburg, and past the Great Bay hotel, take a left before the creek, go 50 feet. On your left is a house where Grandma's family has a BBQ every Sunday. You can join the family for 7 or 8 dollars. Also right next to that is a little Chinese market which is actually very well stocked. Fresh milk, even. It's more expensive that the Afoo supermarket in town, or the Supermarche up the Bush Road, but it's one heck of a lot closer to Divi when you are carrying a backpack full of groceries.
Or continue up that way, way up the Bush Road. On the left is a BBQ place in an old Chinese restaurant called Lido. (same owners as the place I've described above.) Excellent. Maybe 8 dollars. On the right, the Jamaican Jerk. 7 or 8 dollars. Both about a 35 minute hike from Divi.
On the other side of Pburg, try the Cariibean Fruit Stand on Backstreet cattycorner from Lucy Guest House. Again, 7 or 8 dollars.
As you walk back from Pburg towards Divi, follow the Back Street. On the north side is a bakery where they sell not only bread, but ice-cream, and beer, real cheap..they also have incredible meat pies. Buy a bunch of them and bring them back to Divi for lunch.
Or, catch the Marigot bus from Phillipsburg, go to the waterfront park..there are many choices, but my favorite is the Grillade Antillees, again about 7 or 8 Euro.
In Grand Case, Talk of the Town is right on the water, and excellent and cheap, but frankly, the food at Felicia's Lolo on the road coming into town, on the left hand side one block south of the main drag, is somewhat better and even more affordable.
Val's pizzeria in Grand Case is also not to be believed.
Those are my favorite cheap eats on the island. There are more expensive, but none better.