Irazu Volcano is only an hour away from San Jose. One can see Black-capped Flycatcher, Flame-throated Warbler, Black-thighed Grosbeak and a few other highland birds rather easily. Volcano Junco is usually found near the crater. A restaurant near the entrance has hummingbird feeders and can usually produce Volcano, Talamanca, and Fiery-throated Hummingbirds.
Irazu is also a good place to observe the Central American race of the Hairy Woodpecker - a significantly smaller and browner version of the Hairy Woodpecker observed in the United States. Acorn Woodpeckers are also fairly common.
I have also seen Resplendent Quetzal, Costa Rican Pygmy Owl, and both Silky-Flycatchers while stopping on one of the bridges and birding the bridge edges. It's an easy place for highland species especially if you are pressed for time. It's one of the few places where Buffy-crowned Wood-partridges are sometimes seen, but it's not easy.