It's been a few years for us but we keep thinking about going back because it really is a wonderful, low key, homey island. So, quickly:

1. Use Centerline or Judi of Croix for car rentals. They're both local operations and very good. No need for a Jeep or anything if you don't want one--the roads are horrible but not particularly steep, so a small car is great for dodging potholes and finding parking.
2. St. Croix is big enough to have actual farms and a few large grocery stores. There are Saturday farmers markets on both ends of the island, and some big stores: Plaza Extra East and The Market (formerly Plaza Extra West), Cost U Less, a couple of Pueblos, and the Seaside Market and Deli in Christiansted (which is more expensive but has some higher end stuff). You can buy fish at a stand right next to the water in Frederiksted most days. Pretty normal (high) island prices, but seriously cheap rum.
3. We generally don't do a lot of fine dining, but St. Croix has a bunch of super restaurants at the upper end of the scale. I hear a lot about Savant and AMA. For local, tasty stuff, go to the La Reine Chicken Shack, the Love Croix Helados and Eatz truck near Plaza Extra East, and take your choice of a bunch of roti joints in Christiansted. The Montpellier Domino Club has local food and beer drinking pigs. Flyers has moved to Frederiksted, but is a solid choice. Rhythms at Rainbow Beach and Leatherback Landing at Cane Bay are great casual beach joints. And be sure to stop by Armstrong's Ice Cream if you're out west--it's made in-house and has lots of great flavors like Guava, Mango, and Soursop in addition to the usual.
4. There are lots of great things to do there: the Whim Plantation museum, a botanical garden, distillery tours (Cruzan may reopen soon, but you can go to Mutiny Island Vodka and maybe Captain Morgan if not). There are some sunset sails, plus a lot of Buck Island tours if you want to do some snorkeling--or just stay on the boat for the snorkeling part and have fun on the beach later.
5. Gotostcroix.com has a lot of good info, but if your brother-in-law chose to buy there I'm sure he'll have a lot of great recommendations!