US dollars are accepted easily as widely as Bajan dollars, but I always bring Bajan, as it saves on having to make currency conversions.
As to recommendations...
The people are the best thing about the island - friendly, fun, welcoming & laid-back. The joy of the island is the ease of getting out & about, not staying at your hotel.
Their food is fantastic, and the seafood especially - ensure to try the national dish of flying fish, it’s beautiful - and they like mac’n’cheese also, for some reason. I’m pretty much addicted to the yellow Bajan hot sauce you’ll see everywhere.
In terms of restaurants, The renowned Cliff & Tides are expensive but excellent. Nishi (Asian fusion), Lone Star (a past favourite of Michael Winner) & The Fishpot are all good and a little bit less expensive. I like the Beach House for value (and like a lot of places, it’s on the beach and thus you may see baby turtles hatching & migrating to the sea), and Mullins is laid-back. Spago is a good Italian. If you want something informal or light, then Cafe Moyà or the local Just Grillin’ chain are decent.
Banks beer is an institution, and it’s fun to call into the local roadside beer shacks.
Mount Gay Rum is of course made in the island, and the tour is worthwhile - not only do you get some booze, but also a decent meal there.
If you can, try and experience one of the local buses - they play loud local music and are marvellously informal about how they do business and rattle along the roads.
If you don’t have the kids with you, then a day-trip on the ‘Jolly Roger’ is a must. It’s a boat with staff dressed as pirates that leaves from near Bridgetown, and you pay one fee for your meal and unlimited drinks onboard (very, very dangerous). On the way out they drop anchor off Sandy Lane, and you can swim with turtles, snorkel a ship wreck, or just be made to walk the ship’s plank. On the way back they crank the music up loud, and the lethal rum punch kicks in, as most are plastered & dancing.
For the best waves, try Crane Beach on the East, Atlantic of the island, it can get very rough, and you can jump from the cliffs (but it can be blighted with seaweed, so check that before you visit). Snorkelling and other water sports are excellent.
For cricket fans, Kensington Oval is easy to visit, and often there will be local games on.
For kids, the Harrison caves are good. Near the airport you can also visit onboard a Concord left behind.
Bridgetown has several watch stores, and it’s a low-key capital, where you can grab a beer and watch turtles in the harbour. Holetown has a swanky shopping complex as well, and opposite there’s a little rabbit-warren of nice restaurants. The Chattel Town shacks in Holetown would also be popular with your wife for shopping.