Hi Robin,
The significant other and I have only been to Cuba once, which precludes me making any comparisons between places; but for “low-hassle” birding there, we found Playa Larga (on the south coast, top of the Bay of Pigs) to be a really good destination. We went there for seven days in (egad!) 1997, on a really cheap (under $1000 each) all-inclusive package. The hotel was really quite pedestrian, but who cares – we flew into Varadero, were taken directly there by mini-bus, and were able to bike (or walk) to some really good birds.
There was also a guide employed by the hotel, whose job (it seemed) was to take people like us around, at no extra charge (I doubt this is true any more, though – we tipped him by sending him a couple of field guides, which are really hard to come by in Cuba). The only extra we paid for was a bus ride into the Cienaga Zapata – to look at Flamingoes and Spoonbills! (In other words, not the “good” part that has the wren....) Hardly worth it, although we did also see Yellow-headed Warbler along the way, which we didn't see anywhere else.
Just around the hotel, there's lots of short forest, with tracks through it – we found the trogon, the tody, the pygmy-owl, Bee Hummingbird, and a bunch of other endemics, within a short bike ride of the hotel.
I see on the Interweb that the Playa Larga is still operating, and so you could probably still go there - but I'm sure much will have changed in 18 years, so there may be better options now.
Cheers,