Birding the Osa Peninsula has several things to recommend it, but it is a far stretch for a car drive. Getting to any good birding location on the Osa is at least 6 hours from San Jose. The two most frequently visited places for birding are Esquinas Rainforest Lodge and Bosque del Rio Tigre Lodge. Both lodges will likely provide looks at the endemic Black-cheeked Ant-Tanager and some good birding on the forested trails.
Esquinas Rainforest Lodge is on the periphery of the peninsula closer to the main highway and is not as far a drive. You also have a few birding sites around Esquinas within a short car drive. Most hard birders still go to Bosque del Rio Tigre, however, even though the drive is longer and the lodging more spartan.
Bosque del Rio Tigre lodge is also one of the few places (or perhaps the only place) where you can get an adequate visual sighting of a Little Tinamou which can sometimes come close to the lodge. Add birds like Marbled Wood-Quail and Black-cheeked Ant-Tanager to the math, and you have a special place.
Brown-hooded Parrot - Lora Render
Other birds you have a good shot at seeing at Bosque del Rio Tigre are Black-faced Anthrush, White-throated Crake, Scarlet Macaw, Bronzy Hermit, White-tipped Sicklebill, Charming Hummingbird, Red-rumped Woodpecker, Black-striped and Long-tailed Woodcreepers, White-throated Shrike-Tanager, Red-breasted Blackbird and perhaps Uniform Crake if you're there in the dry season. There are not a lot of antbirds in southwestern Costa Rica, but of the ones found on the Osa Peninsula, I saw nearly all of them at Bosque. Plus, the endemic Mangrove Hummingbird can almost always be found on a short drive to the coast if Abraham is guiding.
Bosque del Rio Tigre
Bosque del Rio Tigre lodge is fairly small and only has minimal use of electricity - making it a true eco-lodge by design. The accommodations are spartan but clean. There may be some minimal discomfort at night if the weather is very warm. You wouldn't want to take a non-birder or anyone other than a committed bio-bum, as the action is all in the surrounding habitat. But Bosque del Rio Tigre is clean, has good management, good service and good food .... and the birds are excellent.