Easily the best known of the three local cloud forests, Monteverde has a lot to offer. Best to reserve tickets in advance. Pay attention on their website, as you buy tickets to different parts/trails of the park, with timed entry for each. If you want to do more than one trail, you will need more than one ticket. Also note they may turn you away if you arrive later than your scheduled time. Monteverde is accessible by public bus several times a day from the center, by scheduled transport 4-5 times daily, private car or transport, and even by walking - it's a decent distance from the center of town, but there are sidewalks most of the way along the main route.
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Children's Eternal Rainforest is the largest private reserve in Costa Rica, and Bajos del Tigre is the entry station by Santa Elena. This part is still cloud forest, but just a bit drier / less humid than the other two on the list.
Monteverde Waterfall
A waterfall, located between the center of town and the Monteverde Cloud Forest Reserve. It's about a 15-20 min hike each way to/from the waterfall.
Free hike just east of town. Starts behind the gas station. Steep hike with a nice view at the top, weather permitting.
Monteverde Sunset Viewpoint
This viewpoint is literally on the side of the road, on the right just past Ona's Cafe (if you're heading out of town). Four benches, easy to miss if you're not looking for it. Great view out across the valley, facing west which makes it perfect for sunset viewing (but worth a quick stop any time of day).
Monteverde Butterfly Gardens
Ficus La Raiz is a natural oddity. A Ficus tree fell down across an opening above a stream, and didn't die but continued growing. Now the roots form a natural bridge as they cross the stream and reach down towards the water below. It's cute, it's quirky, it's cheap - worth stopping by if you have spare time in your day. Bring exact change - money is collected in an honor-system donation box where the trail starts in the parking lot. This is on private property, so please be respectful of the space and the people who live there.