Carara NP, Tarcoles River, and Vicinity
I've been to Carara National Park several times on short visits. I had a guide twice specifically for a few deep-forest birds. Carara is both accessible and productive as a birding location. It shouldn't be missed. The general area includes the collision of two ecological zones - the drier scrub vegetation found in Guanacaste to the north and the Pacific rainforest found to the south. As a region, the area is perhaps the most diverse area in Costa Rica.
The main trail is usually known as the Headquarters Trail right near the park headquarters. This is deep forest and the birds can be quiet. It's the best trail for Black-faced Anthrush, Streak-chested Antpitta, Scaly-throated Leaf-tosser, Red-Capped and Blue-crowned Manakins, Spot-crowned Euphonia, and several woodcreepers. This is the only spot in Costa Rica where I have observed Black-tailed Flycatcher - a much trickier bird than its close relative, the Sulphur-rumped Flycatcher. A personal guide is valuable on this trail.
One might also drive to the Tarcoles River bridge not far up the road from Carara. The big selling point of the bridge is the crocodile activity below it. However, I've seen Yellow-headed Caracara, Yellow-billed Cotinga, and King Vulture from the bridge as well as Cabanis's Wren below it. Raptors and marsh birds are also possible.
If you had hired a guide service, you might also be able to visit Guacalillo Road nearby which has easy access to some drier pastureland habitat. This road could produce birds like Long-tailed Manakin, White-throated Magpie-Jay and Turquoise-browed Motmot.
Finally, if you have time, you might wish to take a short boat trip of the Tarcoles River where you can pick up some mangrove-specific birds like Boat-billed Heron, Mangrove Hummingbird, Mangrove Swallow, and Mangrove Vireo. Occasionally, rails are seen from the boat trip.